Skip to content. Skip to main navigation.

avatar

Ren-Cang Li

Name

[Ren-Cang Li]
  • Professor, Mathematics

Biography

Ren-Cang Li is a Professor of Mathematics at UT Arlington. He received his BS in Computational Mathematics from Xiamen University in 1985 and his MS also in Computational Mathematics from Chinese Academy of Science in 1988 and his Ph.D. in Applied Mathematics from UC Berkeley in 1995. He joined ORNL in 1995 as a Householder Fellow and moved to University of Kentucky in 1996 as an assistant and then associate professor, and moved to the University of Texas at Arlington as a professor in 2006. He was awarded a Friedman memorial prize in Applied Mathematics from UC Berkeley in 1996, a CAREER award from NSF in 1999, and a distinguished paper award from the International Consortium of Chinese Mathematicians (ICCM) in 2018. He helped HP in developing its libm library for HP Itanium computers in 2001. His research interest includes floating-point support for scientific computing, numerical linear algebra, reduced order modeling, nonlinear manifold learning, large scale eigenvalue computations in electronic structure calculations, and unconventional schemes for ordinary differential equations.

Education

    • 1998 MS in Matrix Computations
      Chinese Academy Of Sciences, 1998
    • 1995 PhD in Applied Mathematics
      Univ of Calif Berkeley, 1995
    • 1985 BS in Computational Mathematics
      Xiamen University, 1985

Appointments

    • Sept 2006 to Present Professor
      Mathematics ,University of Texas at Arlington (Arlington, TX,
    • Sept 1995 to May 2006 Assistant/Associate Professor
      Mathematics ,University of Kentucky (Lexington, KY,
    • Aug 1995 to Dec 1996 Householder Fellow in Scientific Computing
      Oak Ridge National Laboratory (Oak Ridge, TN, United States)

Memberships

    • 1993 to Present Society of Applied and Industrial Mathematics

Awards and Honors

    • Oct  2019 2019 Data Mining Best General Paper Competition sponsored by INFORMS Data Mining
    • Dec  2018 Distinguished Paper Award sponsored by International Consortium of Chinese Mathematicians
    • May  1999 NSF CAREER sponsored by NSF
    • May  1996 Friedman memorial prize in Applied Mathematics sponsored by University of California at Berkeley
    • Aug  1995 The 1995 Householder Fellow in Scientific Computing sponsored by Oak Ridge National Laboratory

Other Activities

      • Feb 2003
        (Idaho)
        HP

Publications

      Journal Article 2019
      • An Efficient Numerical Method for the Symmetric Positive Definite Second-Order Cone Linear Complementarity Problem
        [Wang, Xiang, Li, Xing, Zhang, Lei-Hong , Li, Ren-Cang ]. Journal of Scientific Computing. 79(3), 1608-1629.
      2019
      • Highly Accurate Doubling Algorithm for Quadratic Matrix Equation from Quasi-Birth-and-Death Process
        [Cai, Cairong, Li, Ren-Cang, Ma, Changfeng ]. Linear Algebra and Its Applications. 583, 1-45.
      2019
      • Perturbation Analysis For Matrix Joint Block Diagonalization
        [Cai, Yunfeng, Li, Ren-Cang]. Linear Algebra and Its Applications. 581, 163-197.

      Book 2018
      • Structure-Preserving Doubling Algorithms For Nonlinear Matrix Equations
        [Huang, Tsing-Ming, Li, Ren-Cang, Lin, Wen-Wei]. Philadelphia: "SIAM".

      Journal Article 2018
      • On an Eigenvector-Dependent Nonlinear Eigenvalue Problem
        [Cai, Yunfeng, Zhang, Lei-hong , Bai, Zhaojun, Li, Ren-Cang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 39(3), 1360-1382.
      2018
      • Structured Backward Error for Palindromic Polynomial Eigenvalue Problems, II: Approximate Eigentriplets
        [Liu, Changli, Li, Ren-Cang]. Frontiers of Mathematics in China. 13(6), 1397-1426.

      Journal Article 2017
      • A Symmetric Structure-Preserving ΓQR Algorithm for Linear Response Eigenvalue Problems
        [Li, Ren-Cang, Li , Tiexiang , Lin, Wen-Wei ]. Linear Algebra and Its Applications.(520), 191-214.
      2017
      • Error Bounds For Approximate Deflating Subspaces For Linear Response Eigenvalue Problems
        [Wang, Wei-guo, Zhang, Lei-hong , Li, Ren-Cang]. Linear Algebra and Its Applications. 528, 273-289.
      2017
      • Highly Accurate Doubling Algorithms for M-matrix Algebraic Riccati Equations
        [Li, Ren-Cang, Xue, Jungong ]. Numerische Mathematik.(37), 733-767.
      2017
      • On the Generalized Lanczos Trust-Region Method
        [Zhang, Lei-hong, Shen, Chungen, Li, Ren-Cang]. SIAM Journal on Optimization : A Publication of the Society for Industrial and Applied Mathematics. 27(3), 2110-2142.
      2017
      • Optimal Parameters for Doubling Algorithms
        [Huang, Tsing-Ming, Li, Ren-Cang, Lin, Wen-Wei, Lu, Linzhang]. Journal of Mathematical Study. 50(4), 339-357.

      Journal Article 2016
      • A Block Chebyshev-Davidson Method for Linear Response Eigenvalue Problems
        [Li, Ren-Cang, Teng, Zhongming , Zhou, Yunkai ]. Advances in Computational Mathematics. 42(5), 1103-1128.
      2016
      • A Fast Algorithm For Fast Train Palindromic Quadratic Eigenvalue Problems
        [Li, Ren-Cang, Lu, Linzhang , Wang, Teng , Kuo, Yueh-Cheng, Lin, Wen-Wei ]. SIAM Journal on Scientific Computing : A Publication of the Society for Industrial and Applied Mathematics. 38(6), A3410-A3429.
      2016
      • A New Two- Phase Structure-Preserving Doubling Algorithm for Critically Singular MMatrix Algebraic Riccati Equations
        [Li, Ren-Cang, Huang, Tsung-Ming , Huang, Wei-Qiang , Lin, Wen-Wei ]. Numerical Linear Algebra with Applications.(23), 291-313.
      2016
      • A Nonlinear QR Algorithm for Unstructurally Banded Nonlinear Eigenvalue Problems
        [Li, Ren-Cang, Garrett , C. Kristopher , Bai, Zhaojun ]. ACM Transactions on Mathematical Software. 43(1), 4:1-4:19.
      2016
      • Linear Response Eigenvalue Problem Solved by Extended Locally Optimal Preconditioned Conjugate Gradient Methods
        [Li, Ren-Cang, Bai , Zhaojun , Lin, Wen-Wei ]. SCIENCE CHINA Mathematics. 59(8), 1443-1460.
      2016
      • Locally optimal and heavy ball GMRES methods
        [Li, Ren-Cang]. Japan Journal on Industrial Applied Mathematics. 33(2), 471-499.
      2016
      • Self-Corrective Iterations (SCI) for Generalized Diagonally Dominant Matrices
        [Li, Ren-Cang, Guan, Jinrui , Lu, Linzhang, Shao, Rongxia ]. Journal of Computational and Applied Mathematics.(302), 285-300.

      Book Chapter 2015
      • Recent Progress in Linear Response Eigenvalue Problems
        Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing
        [Bai, Zhaojun, Li, Ren-Cang]. Lecture Notes in Computational Science and Engineering. 117, 287-304. "Springer".

      Other 2015
      • Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems
        [Li, Ren-Cang, Bai, Zhaojun , Gao, Weiguo , Su , Yangfeng ]. Matrix Functions and Matrix Equations. 19, 76-108. "World Scientific".

      Journal Article 2015
      • A Krylov Subspace Method For Large Scale Second Order Cone Linear Complementarity Problem
        [Li, Ren-Cang, Zhang, Lei-Hong , Yang, Wei Hong , Shen, Chungen]. SIAM Journal on Scientific Computing : A Publication of the Society for Industrial and Applied Mathematics. 37(4), A2046-A2075.
      2015
      • A New Look at the Doubling Algorithm for a Structured Palindromic Quadratic Eigenvalue Problem
        [Li, Ren-Cang, Lu , Linzhang , Yuan, Fei ]. Numerical Linear Algebra with Applications.(22), 393-409.
      2015
      • Backward Perturbation Analysis and Residual-based Error Bounds For the Linear Response Eigenvalue Problem
        [Li, Ren-Cang]. BIT Numerical Mathematics. 55(3), 869-896.
      2015
      • Backward Perturbation Analysis and Residual-based Error Bounds For the Linear Response Eigenvalue Problem
        [Li, Ren-Cang, Zhang , Lei-Hong , Lin, Wen-Wei]. BIT Numerical Mathematics. 55(3), 869-896.
      2015
      • Cluster-robust accuracy bounds for Ritz subspaces
        [Li, Ren-Cang, Teng , Zhongming , Lu, Linzhang ]. Electronic Transactions on Numerical Analysis (Online).(44), 624-638.
      2015
      • Convergence of the Block Lanczos Method For Eigenvalue Clusters
        [Li, Ren-Cang, Zhang, Lei-Hong ]. Numerische Mathematik. 131(1), 83-113.
      2015
      • Maximization of the Sum of the Trace Ratio On the Stiefel Manifold, II: Computation
        [Li, Ren-Cang, Zhang, Lei-Hong ]. SCIENCE CHINA Mathematics. 58(7), 1549-1566.
      2015
      • Monotonicity of Unitarily Invariant Norms
        [Li, Ren-Cang, Wang, Xuefeng ]. Linear Algebra and Its Applications.(466), 254-266.
      2015
      • Perturbation of Partitioned Linear Response Eigenvalue Problems
        [Li, Ren-Cang, Teng , Zhongmingand , Lu, Linzhang]. Electronic Transactions on Numerical Analysis (Online).(44), 624-638.
      2015

      Conference Proceeding 2015
      Journal Article 2014
      • Extensions of Wielandt’s Min-max Principles for Positive Semi-Definite Pencils
        [Li, Ren-Cang, Liang, Xin ]. Linear & Multilinear Algebra. 62(8), 1032-1048.
      2014
      • GIP Integrators for Matrix Riccati Differential Equations
        [Li, Ren-Cang, Garrett, Kris ]. Applied Mathematics and Computation.(241), 283-297.
      2014
      • Maximization of the Sum of the Trace Ratio On the Stiefel Manifold, I: Theory
        [Li, Ren-Cang]. SCIENCE CHINA Mathematics. 57(12), 2495-2508.
      2014
      • Minimization Principles and Computation for the Generalized Linear Response Eigenvalue Problem
        [Li, Ren-Cang, Bai, Zhaojun ]. BIT Numerical Mathematics.(54), 31-54.
      2014
      • Rayleigh-Ritz Approximation for the Linear Response Eigenvalue Problem
        [Li, Ren-Cang, Zhang , Lei-Hong , Xue, Jungong ]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics.(35), 765-782.
      2014
      • Simultaneous similarity reductions for a pair of matrices to condensed forms,
        [Li, Ren-Cang, Ye, Qiang]. Communications in Mathematics and Statistics. 2(2), 139-153.

      Journal Article 2013
      • Convergence Analysis of Lanczos-type Methods for the Linear Response Eigenvalue Problem
        [Li, Ren-Cang, Teng, Zhongming ]. Journal of Computational and Applied Mathematics.(247), 17-33.
      2013
      • Deflating Irreducible Singular MMatrix Algebraic Riccati Equations
        [Li, Ren-Cang, Wang , Wei-Guo , Wang, Wei-Chao ]. Numerical Algebra, Control and Optimization. 3(3), 491-518.
      2013
      • Minimization Principle for Linear Response Eigenvalue Problem, II: Computation
        [Li, Ren-Cang, Bai, Zhaojun]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 34(2), 392-416.
      2013
      • Trace Minimization Principles for Positive Semi-Definite Pencils,
        [Li, Ren-Cang, Liang , Xin , Bai, Zhaojun ]. Linear Algebra and Its Applications.(438), 3085-3106.

      Journal Article 2012
      • A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices
        [Li, Ren-Cang, Rocca, Dario , Bai, Zhaojun , Galli, Giulia ]. The Journal of Chemical Physics.(136), 34-111.
      2012
      • A Family of Anadromic Numerical Methods for Matrix Riccati Differential Equations
        [Li, Ren-Cang, Kahan, W. ]. Mathematics of Computation. 81(277), 233-265.
      2012
      • Accurate Solutions of M-Matrix Algebraic Riccati Equations
        [Li, Ren-Cang, Xue, Jungong , Xu, Shu-fang ]. Numerische Mathematik. 120(4), 671-700.
      2012
      • Accurate Solutions of M-Matrix Sylvester Equations
        [Li, Ren-Cang, Xue , Jungong , Xu, Shu-fang ]. Numerische Mathematik. 120(4), 671-700.
      2012
      • Alternating-Directional Doubling Algorithm for M-Matrix Algebraic Riccati Equations
        [Li, Ren-Cang, Wang , Wei-Guoand , Wang, Wei-Chao ]. 33(1), 170-194.
      2012
      • An Interpolating Family of Means
        [Li, Ren-Cang, Bhatia, R. ]. Communications on Stochastic Analysis. 6(1), 15-31.
      2012
      • Minimization Principle for Linear Response Eigenvalue Problem, I: Theory
        [Li, Ren-Cang, Bai, Zhaojun]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 33(4), 1074-1100.
      2012
      • Perturbation of Multiple Eigenvalues of Hermitian Matrices
        [Li, Ren-Cang, Nakatsukasa, Yuji , Truhar, Ninoslav , Wang, Wei-guo ]. Linear Algebra and Its Applications.(437), 202-213.

      Journal Article 2011
      • Bounding the Spectrum of Large Hermitian Matrices
        [Li, Ren-Cang, Zhou, Yunkai ]. Linear Algebra and Its Applications.(435), 480-493.
      2011
      • Multiplicative Perturbation Analysis for QR Factorizations
        [Li, Ren-Cang, Chang, Xiao-Wen ]. Numerical Algebra, Control and Optimization. 1(2), 301-306.
      2011
      • Perturbation of Partitioned Hermitian Generalized Eigenvalue Problem
        [Li, Ren-Cang, Nakatsukasa, Yuji , Truhar, Ninoslav, Xu, Shufang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 32(2), 642-663.
      2011
      • Stable Solutions of Linear Systems Involving Long Chain of Matrix Multiplications
        [Li, Ren-Cang, Bai, Zhaojun, Lee, Roger, Xu, Shu-fang ]. Linear Algebra and Its Applications.(435), 659-673.

      Journal Article 2010
      • Analysis of the solution of the Sylvester equation using Low Rank ADI with exact shifts
        [Li, Ren-Cang, Truhar, Ninoslav , Tomljanovic, Zoran ]. Systems & Control Letters. 59(3-4), 248-257.
      2010
      • Sharpness in Rates of Convergence For Symmetric Lanczos Method
        [Li, Ren-Cang]. Mathematics of Computation. 79(269), 419-435.
      2010
      • Structured Backward Error for Palindromic Polynomial Eigenvalue Problems,
        [Li, Ren-Cang, Lin , W.-W. , Wang, C.-S. ]. Numerische Mathematik. 116(1), 95-122.

      Technical Report 2010 2010
      Instructor's Manual 2009
      • The Rate of Convergence of GMRES on a Tridiagonal Toeplitz Linear System
        [Li, Ren-Cang, Zhang, W.]. Numerische Mathematik.(11), 267-293.

      Journal Article 2009
      • Formally Certified Argument Reduction with a Fused-Multiply-Add
        [Li, Ren-Cang, Boldo , S. , Daumas, M. ]. IEEE Transactions on Computers. 58(8), 1139-1145.
      2009
      • On the ADI Method for Sylvester Equations
        [Li, Ren-Cang, Benner , P. , Truhar, N. ]. Journal of Computational and Applied Mathematics.(233), 1035-1045.
      2009
      • The Rate of Convergence of GMRES on a Tridiagonal Toeplitz Linear System, II
        [Li, Ren-Cang, Zhang, W. ]. Linear Algebra and Its Applications. 431.
        2425-2436

      Other 2008
      • A Unified Krylov Projection Framework for Structure- Preserving Model Reduction
        [Li, Ren-Cang, Bai , Z. , Su, Y., Schilders, W. H. A. , van der Vorst, H. A. , Rommes , J. ]. Model Order Reduction: Theory, Research Aspects and Applications. 13, 75-93.

      Journal Article 2008
      • Hard Cases For Conjugate Gradient Method
        [Li, Ren-Cang]. International Journal for Information & Systems Sciences. 4(1), 15-29.
      2008
      • On Meinardus’ Examples For the Conjugate Gradient Method
        [Li, Ren-Cang]. Mathematics of Computation.(77), 335-352.
      2008
      • Vandermonde Matrices with Chebyshev Nodes
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(428), 1803-1832.

      Journal Article 2007
      • Analysis of An Alignment Algorithm for Nonlinear Dimensionality Reduction
        [Li, Ren-Cang, Ye, Qiang , Zha, Hongyuan]. BIT.(47), 873-885.
      2007
      • Backward Error of Polynomial Eigenproblems Solved by Linearization
        [Li, Ren-Cang, Higham , Nicholas J. , Tisseur, Franc¸oise ]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 29(4), 1218-1241.
      2007
      • Convergence of CG and GMRES on a Tridiagonal Toeplitz Linear System
        [Li, Ren-Cang]. BIT.(47), 577-599.
      2007
      • Eigenvalues of An Alignment Matrix in Nonlinear Manifold Learning
        [Li, Ren-Cang]. Communications in Mathematical Sciences. 5(2), 313-329.
      2007
      • Matrix Perturbation Theory
        [Li, Ren-Cang, Hogben, L. , Brualdi, R. , Greenbaum , A. , Mathias , R. ]. Handbook of Linear Algebra. New York: "Chapman & Hall/CRC".

      Conference Proceeding 2006
      • Structure-Preserving Model Reduction, Proceedings of PARA’04
        [Li, Ren-Cang, Bai, Zhaojun , Dongarra, J. , Madsen, K. , Wa´sniewski , J. ].(3732), 323-332. "Springer".

      Journal Article 2006
      • Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix
        [Li, Ren-Cang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 28(3), 829-844.
      2006
      • Krylov type subspace methods for matrix polynomials
        [Li, Ren-Cang, Hoffnung , L. , Ye, Q. ]. Linear Algebra and Its Applications.(415), 52-81.
      2006
      • Lower bounds for the condition number of a real confluent Vandermonde matrix
        [Li, Ren-Cang]. Mathematics of Computation.(75), 1987-1995.

      Journal Article 2005
      • A note on eigenvalues of perturbed Hermitian matrices
        [Li, Ren-Cang, Li, Chi-Kwong ]. Linear Algebra and Its Applications.(395), 183-190.
      2005
      • Relative perturbation bounds for positive polar factors of graded matrices
        [Li, Ren-Cang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics.(27), 424-433.
      2005
      • Structure-preserving model reduction using a Krylov subspace projection formulation
        [Li, Ren-Cang, Bai, Z. ]. Communications in Mathematical Sciences. 3(2), 179-199.

      Technical Report 2005
      • Sharpness in Rates of Convergence For CG and Symmetric Lanczos Methods
        [Li, Ren-Cang]. Technical Report.

      Journal Article 2004
      • Accuracy of computed eigenvectors via optimizing a Rayleigh quotient
        [Li, Ren-Cang]. BIT. 44(3), 585-593.
      2004
      • Near optimality of Chebyshev interpolation for elementary function computations
        [Li, Ren-Cang]. IEEE Transactions on Computers.(53), 678-687.
      2004
      • The ABC conjecture and correctly rounded reciprocal square roots
        [Li, Ren-Cang, Croot , Ernie , Zhu, Hui June ]. Theoretical Computer Science.(315), 405-417.

      Technical Report 2004
      • Structural preserving model reductions
        [Li, Ren-Cang]. Technical Report.

      Conference Proceeding 2003
      • Theorems on efficient argument reductions
        [Li, Ren-Cang, Boldo , S. , Daumas, M. ]. Proceedings of the 16th IEEE Symposium on Computer Arithmetic. 129-136.

      Journal Article 2003
      • A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems
        [Li, Ren-Cang, Ye, Qiang ]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics. 25(2), 405-428.
      2003
      • A theorem for graded indefinite hermitian matrices
        [Li, Ren-Cang, Truhar, Ninoslav ]. Linear Algebra and Its Applications.(359), 263-276.
      2003
      • On perturbations of matrix pencils with real spectra, a Revisit
        [Li, Ren-Cang]. Mathematics of Computation.(72), 715-728.

      Journal Article 2002
      • Pinchings and norms of scaled triangular matrices
        [Li, Ren-Cang, Kahan , W. , Bhatia, R. ]. Linear & Multilinear Algebra.(50), 15-21.

      Other 2000
      • Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide
        [Li, Ren-Cang, Bai, Z. , Demmel, J. , Dongarra, J. , Ruhe, A. , van der Vorst , H. ]. SIAM.

      Journal Article 2000
      • A new relative perturbation theorem for singular value problem
        [Li, Ren-Cang, Stewart, G. W. ]. Linear Algebra and Its Applications.(313), 41-51.
      2000
      • Relative perturbation theory: IV sin2θ Theorems
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(311), 45-60.

      Technical Report 2000
      • Unconventional reflexive numerical methods for matrix differential riccati equations
        [Li, Ren-Cang]. Technical Report.
      2000
      • Unconventional reflexive numerical methods for matrix differential riccati equations
        [Li, Ren-Cang]. Technical Report. Department of Mathematics, University of Kentucky.
      2000
      • Test positive realness of a general transfer function matrix
        [Li, Ren-Cang]. "Department of Mathematics, University of Kentucky".

      Conference Proceeding 2000
      Journal Article 1999
      • A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory
        [Li, Ren-Cang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics.(21), 440-445.
      1999
      • Relative perturbation theory: II eigenspace and singular space variations
        [Li, Ren-Cang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics.(20), 471-492.

      Journal Article 1998
      • Eigenvalues of Symmetrizable Matrices
        [Li, Ren-Cang, Bhatia, R. , Kittaneh, F. ]. BIT.(38), 1-11.
      1998
      • Relative perturbation theory: I eigenvalue and singular value variations
        [Li, Ren-Cang]. SIAM Journal on Matrix Analysis and Applications : A Publication of the Society for Industrial and Applied Mathematics.(19), 956-982.
      1998
      • Spectral variations and Hadamard products: some problems
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(278), 317-326.

      Technical Report 1998
      • A multi-resolution approach for calculating primary eigenvectors of a large set of images
        [Li, Ren-Cang]. Technical Report. Department of Mathematics, University of Kentucky.

      Journal Article 1997
      • Composition constants for raising the orders of unconventional schemes for ordinary differential equations
        [Li, Ren-Cang, Kahan, W. ]. Math. Comp.(66), 1089-1099.
      1997
      • Relative perturbation bounds for the unitary polar factor
        [Li, Ren-Cang]. BIT.(37), 67-75.
      1997
      • Relative perturbation theory: (III) more bounds on eigenvalue variation
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(266), 337-345.
      1997
      • Some inequalities for commutators and an application to spectral variation. II
        [Li, Ren-Cang]. Linear & Multilinear Algebra.(43), 207-219.
      1997
      • Unconventional schemes for a class of ordinary differential equations—with applications to the Korteweg-de Vries (KdV) equation
        [Li, Ren-Cang, Kahan, W. ].(134), 316-331.

      Journal Article 1996
      • A sharp version of Kahan’s theorem on clustered eigenvalues
        [Li, Ren-Cang, Cao , Z.-H. , Xie, J.-J. ]. Linear Algebra and Its Applications.(245), 147-156.
      1996
      • On perturbations of matrix pencils with real spectra, II
        [Li, Ren-Cang, Bhatia, R. ]. Math. Comp..(65), 637-645.
      1996
      • On perturbations of matrix pencils with real spectra, II
        [Li, Ren-Cang]. Math. Comp..(65), 637-645.

      Journal Article 1995
      • New perturbation bounds for the unitary polar factor
        [Li, Ren-Cang]. SIAM J. Matrix Anal. Appl.(16),

      Journal Article 1994
      • On eigenvalue variations of Rayleigh quotient matrix pencils of a definite pencils
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(208-209), 471-483.
      1994
      • On perturbations of matrix pencils with real spectra
        [Li, Ren-Cang]. Math. Comp.(62), 231-265.

      Technical Report 1994
      • An efficient tridiagonal eigenvalue solver on CM 5 with Laguerre’s iteration
        [Li, Ren-Cang]. Technical Report. Computer Science Division, University of California at Berkeley.
      1994
      • Linear systems with coefficient matrices having fields of values not containing the origin
        [Li, Ren-Cang]. Technical Report. Computer Science Division, University of California at Berkeley.
      1994
      • Relations between the field of values of a matrix and those of its Schur complements
        [Li, Ren-Cang]. Technical Report. Computer Science Division, University of California at Berkeley.
      1994
      • Solving secular equations stably and efficiently
        [Li, Ren-Cang]. Technical Report. Computer Science Division, University of California at Berkeley.

      Journal Article 1993
      • A perturbation bound for definite pencils
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(179), 191-202.
      1993
      • A perturbation bound for the generalized polar decomposition
        [Li, Ren-Cang]. BIT.(33), 304-308.
      1993
      • Bounds on perturbations of generalized singular values and of associated subspaces
        [Li, Ren-Cang]. SIAM J. Matrix Anal. Appl..(14), 195-234.
      1993
      • Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(182), 199-234.

      Journal Article 1992
      • Algorithms for inverse eigenvalue problems
        [Li, Ren-Cang]. J. Comp. Math.(10), 97-111.
      1992
      • Compute multiple nonlinear eigenvalues
        [Li, Ren-Cang]. J. Comp. Math. 10(1), 1-20.
      1992
      • On eigenvalues of a Rayleigh quotient matrix
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(169), 249-255.
      1992
      • Solution of linear matrix equation AXD − BXC = S and perturbation of eigenspaces of a matrix pencil
        [Li, Ren-Cang]. J. Comp. Math.(10), 93-109.

      Journal Article 1990
      • Computing the Critical Points of a Stability Problem
        [Li, Ren-Cang].
      1990
      • On the variations of the spectra of matrix pencils
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(139), 147-164.

      Journal Article 1989
      • On perturbation theorems for the generalized eigenvalues of regular matrix pencils
        [Li, Ren-Cang]. J. Numer. Math. Appl.. 11, 24-35.
      1989
      • Perturbation bounds for generalized eigenvalues.
        [Li, Ren-Cang]. J. Numer. Math. Appl.(11), 1-9.
      1989
      • Perturbation bounds for generalized eigenvalues. II
        [Li, Ren-Cang]. Chinese J. Numer. Math. Appl..(11), 39-43.
      1989
      • QR decomposition and nonlinear eigenvalue problems
        [Li, Ren-Cang].

      Journal Article 1988
      • A converse to the Bauer-Fike type theorem
        [Li, Ren-Cang]. Linear Algebra and Its Applications.(109), 167-178.

      Software Unknown Unknown Unknown
      • Contribution to LAPACK: FORTRAN subroutines for solving secular equations which sit at the kernel of the divide-and-conquer methods for the symmetric eigenvalue problem and singular value problem
        [Li, Ren-Cang]. ???? (1925).
      Unknown
      • Formal definitions and theorems, with proofs, about floating-point numbers
        [Li, Ren-Cang, Boldo, Sylvie , Daumas, Marc , Fousse, Laurent , Li, Ren-Cang , Melquiond, Guillaume , Muller, Jean-Michel, Rideau, Laurence , Thery, Laurent ] (1925).
        www.netlib.org/fp/fp2.tgz
      Unknown Unknown

      Journal Article Unknown
      • Error Bounds For Approximate Deflating Subspaces For Linear Response Eigenvalue Problems
        [Li, Ren-Cang, Wang, Wei-guo , Zhang, Lei-hong ]. Linear Algebra and Its Applications (1925).
      Unknown
      • On the Generalized Lanczos TrustRegion Method
        [Li, Ren-Cang, Zhang , Lei-hong , Shen, Chungen ]. SIAM Journal on Optimization : A Publication of the Society for Industrial and Applied Mathematics (1925).
      Unknown
      • On the Generalized Lanczos TrustRegion Method
        [Li, Ren-Cang, Zhang , Lei-hong , Shen, Chungen ]. SIAM Journal on Optimization : A Publication of the Society for Industrial and Applied Mathematics (1925).
      Unknown
      • Optimal Parameters for Doubling Algorithms
        [Li, Ren-Cang, Huang, Tsung-Ming , Lin, Wen-Wei , Lu, Linzhang ]. Journal of Mathematical Study (1925).

      Other Unknown
      • Perturbation Analysis For Matrix Joint Block Diagonalization
        [Li, Ren-Cang] (1925).
      Unknown
      • Structured Backward Error for Palindromic Polynomial Eigenvalue Problems, II: Approximate Eigentriplets
        [Li, Ren-Cang, Liu, Changli]. ???? (1925).

      Technical Report Unknown
      • Reciproot algorithm–correctly rounded?
        [Li, Ren-Cang]. Technical Report (1925). Computer Science Division, University of California at Berkeley.

Presentations

    • June  2019
      Li, Ren-Cang, "Perturbation Analysis for Matrix Joint Block Diagonalization", Guilin University of Electronic Technology, Guilin, China. (June 8, 2019).
    • May  2019
      Li, Ren-Cang, "Convergence of Lanczos Methods for Trust-Region Subproblem", Jeju National University, Korea, Jeju, Korea. (May 24, 2019).
    • December  2018
      Li, Ren-Cang, "A Krylov Subspace Method for Large-Scale Second-Order Cone Linear Complementarity Problem", National Taiwan University, Taiwan. (December 29, 2018).
    • December  2018
      Li, Ren-Cang, "Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation", Fudan University, Shanghai, China. (December 16, 2018).
    • August  2018
      Li, Ren-Cang, "On an Eigenvector-Dependent Nonlinear Eigenvalue Problem", Guizhou University, Guizhou, China. (August 5, 2018).
    • June  2018
      Li, Ren-Cang, "Highly Accurate Doubling Algorithm for Quadratic Matrix Equations from Quasi-Birth-And-Death Process", Shanghai University, Shanghai, China. (June 9, 2018).
    • October  2017
      Li, Ren-Cang, "Eigenspace Perturbation and Nonlinear Eigenvalue Problems", Fudan University, Shanghai, China. (October 21, 2017).
    • October  2016
      Li, Ren-Cang, "Ubiquitous Doubling Algorithms, General Theory, and Applications", CIRM, France. (October 28, 2016).
    • August  2016
      Li, Ren-Cang, "• Ubiquitous Doubling Algorithms, General Theory, and Applications", Shanghai University. (August 10, 2016).
    • July  2016
      Li, Ren-Cang, "• Highly Accurate Doubling Algorithms for M-matrix Algebraic Riccati Equations", Leuven, Belgium. (July 15, 2016).
    • June  2016
      Li, Ren-Cang, "• Nonlinear Eigenvalue Problems from Maximizing Sum of Trace Ratios", Beijing International Center for Mathematical Research . (June 24, 2016).
    • June  2016
      Li, Ren-Cang, "Ubiquitous Doubling Algorithms, General Theory, and Applications", Zagreb, Croatia. (June 14, 2016).
    • October  2015
      Li, Ren-Cang, "• The Big Bang Theory in High Accuracy Computations", University of California at Berkeley. (October 24, 2015).
    • October  2015
      Li, Ren-Cang, "The Big Bang Theory in High Accuracy Computations", University of California at Berkeley. (October 23, 2015).
    • August  2015
      Li, Ren-Cang, "Linear Response Eigenvalue Problem Solved by Extended Locally Optimal Preconditioned Conjugate Gradient Methods", ICIAM 2015, Beijing. (August 14, 2015).
    • June  2015
      Li, Ren-Cang, "Nonlinear Eigenvalue Problems from Maximizing Sum of Trace Ratios", The 2015 Shanghai Graduate Students . (June 27, 2015).
    • August  2014
      Li, Ren-Cang, "Linear Response Eigenvalue Problem Solved by Extended Locally Optimal Preconditioned Conjugate Gradient Methods", Fudan University. (August 12, 2014).
    • August  2014
      Li, Ren-Cang, "Classical Min-Max Principles And Beyond", Sungkyunkwan University, Seoul, Korea. (August 9, 2014).
    • March  2014
      Li, Ren-Cang, "Nonlinear Eigenvalue Problems from Maximizing Sum of Trace Ratios", Tsukuba, Japan. (March 9, 2014).
    • September  2013
      Li, Ren-Cang, "The Hyperbolic Quadratic Eigenvalue Problem", National Tsing-Hua University, Hsinchu, Taiwan. (September 12, 2013).
    • December  2012
      Li, Ren-Cang, "Classical Min-Max Principles and Beyond", Indian Institute of Science, Bangalore, India. (December 30, 2012).
    • August  2012
      Li, Ren-Cang, "Solving Large Scale Linear Response Eigenvalue Problems", State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Science, Urumqi, Xinjiang, China. (August 18, 2012).
    • July  2012
      Li, Ren-Cang, "Accurate Solution of M-Matrix Algebraic Riccati Equation by ADDA: AlternatingDirectional Doubling Algorithm", Fudan University. (July 20, 2012).
    • June  2012
      Li, Ren-Cang, "Accurate Solution of M-Matrix Algebraic Riccati Equation by ADDA: AlternatingDirectional Doubling Algorithm", Valencia, Spain. (June 22, 2012).
    • March  2010
      Li, Ren-Cang, "Perturbation of Partitioned Hermitian Generalized Eigenvalue Problem", Lexington, KY. (March 28, 2010).
    • July  2009
      Li, Ren-Cang, "Bounds on Solutions of Certain Structured Sylvester Equations ", Zhejiang Forestry University, Hangzhou/Lin’An, China . (July 13, 2009).
    • May  2008
      Li, Ren-Cang, "Integrate Matrix Differential Riccati Equations Whose Solutions May Have Singularities", The University of Texas at Arlington. (May 21, 2008).
    • March  2008
      Li, Ren-Cang, "Eigenvalues of a Perturbed Hermitian Matrix", celebrating of the many decades of accomplishments and the 75th birthdays of Prof. William (Velvel) Kahan and Prof. Beresford Parlett. (March 30, 2008).
    • May  2006
      Li, Ren-Cang, "Accurate Computations of Positive Polar Factors of Graded Matrices", Pennsylvania State University, University Park. (May 25, 2006).
    • June  2005
      Li, Ren-Cang, "Rectangular Vandermonde Matrices and Convergence of Krylov Subspace Methods", Regina, Canada. (June 29, 2005).
    • June  2004
      Li, Ren-Cang, "Structural preserving model reductions", Technical University of Denmark, Copenhagen, Denmark. (June 23, 2004).
    • March  2004
      Li, Ren-Cang, "Structural preserving methods for large eigenvalue problems", GAMM, Dresden, Germany. (March 27, 2004).
    •  2003
      Li, Ren-Cang, "Krylov type subspace methods for quadratic matrix polynomials", Williamsburg. ( , 2003).
    • June  2002
      Li, Ren-Cang, "The abc conjecture and correctly rounded reciprocal square roots", Portland, Oregon, USA. (June , 2002).
    • June  2002
      Li, Ren-Cang, "Krylov type subspace methods for quadratic matrix polynomials", Peebles, Scotland. (June 21, 2002).
    • August  2000
      Li, Ren-Cang, Rayens, William , Andersen, Anders, Blonder, Lee , "Mathematical problems in the application of multilinear models to facial emotion processing experiments", Optical Science and Technology, San Diego. (August , 2000).
    • July  2000
      Li, Ren-Cang, Rayens, William , "Kronecker canonical forms and the I×J×2 trilinear model", Denmark. (July , 2000).
    • July  2000
      Li, Ren-Cang, Ravens, William, "Trilinear decomposition and its applications", Puerto Rico. (July 14, 2000).
    • June  1999
      Li, Ren-Cang, "A multi-resolution approach for calculating primary eigenvectors of a large set of images", Chateau Whistler, Whistler, B.C., Canada. (June 18, 1999).
    • July  1998
      Li, Ren-Cang, "Unconventional reflexive numerical methods for matrix differential riccati equations", MATHEMATICAL THEORY OF NETWORKS AND SYSTEMS (MTNS 98), Padavo, Italy. (July 10, 1998).
    • May  1998
      Li, Ren-Cang, "A multi-resolution approach for calculating primary eigenvectors of a large set of images", Canadian Applied Mathematics Society, Vancouver, British Columbia, Canada. (May 31, 1998).
    • November  1997
      Li, Ren-Cang, "Spectral variation for diagonalizable matrices", Snowbird Ski & Summer Resort, Snowbird, UT. (November 1, 1997).
    • July  1997
      Li, Ren-Cang, "Unconventional reflexive numerical methods for matrix differential riccati equations", Stanford, CA. (July 18, 1997).
    • July  1997
      Li, Ren-Cang, "Unconventional reflexive numerical methods for matrix differential riccati equations", Stanford, CA. (July 18, 1997).
    • November  1996
      Li, Ren-Cang, "Unconventional schemes for ordinary differential equations", ODE to Linear Algebra and Rational Approximation, Monterey, CA. (November 2, 1996).
    • August  1996
      Li, Ren-Cang, "Eigenvalues of symmetrizable matrices", Germany. (August 17, 1996).
    • July  1996
      Li, Ren-Cang, "Raising the orders of unconventional schemes for ordinary differential equations", Kansas City, Missouri. (July 26, 1996).
    • July  1996
      Li, Ren-Cang, "Sensitivity analysis for polar decompositions", Kansas City. (July 26, 1996).
    • June  1996
      Li, Ren-Cang, Kahan, W. (Presenter), "Relative perturbation theory for eigenvalue problem", Switzerland. (June 21, 1996).
    •  1990
      Li, Ren-Cang, "Bounds on perturbations of generalized singular values and of associated subspaces", Switzerland. ( , 1990).

Support & Funding

This data is entered manually by the author of the profile and may duplicate data in the Sponsored Projects section.
    • Sept 2016 to Aug 2020 An Innovative Bridge Program for Mentoring BS-MS Fast-Track Students towards PhDs in Mathematical Sciences sponsored by  - $585001
      (Funded)
    • Aug 2017 to Aug 2020 Ubiquitous Doubling Algorithms For Nonlinear Matrix Equations and Applications sponsored by  - $200822
      Ren-cang Li (Funded)
    • July 2015 to June 2019 AF: Small: Collaborative Research: Mathematical Theory and Fast Algorithms for Rayleigh Quotient-type Optimizations sponsored by  - $138995
      Ren-cang Li (Funded)
    • Sept 2013 to Aug 2017 Linear Response Eigenvalue Problem: New Minimization Principles and Efficient Algorithms sponsored by  - $214458
      Ren-cang Li (Funded)
    • Sept 2011 to Aug 2014 Collaborative Research: Efficient Solvers for Nonlinear Eigenvalue Problems and Applications sponsored by  - $169941
      Ren-cang Li (Funded)
    • Sept 2008 to Aug 2012 Marching Over Poles: Innovative Ways to Solve Matrix Differential Riccati Equations sponsored by  - $262256
      Ren-cang Li (Funded)
    • June 2006 to July 2009 Structural Preserving Numerical Methods for Eigenvalue Problems sponsored by  - $219790
      Ren-cang Li (Funded)

Students Supervised

    • Aug 2018
      Mei Yang, (Mathematics)
    • Dec 2017
      Gul Karaduman, (Mathematics)
    • Aug 2017
      Ivan Ojeda-Ruiz, (Mathematics)
    • Dec 2016
      Melinda Au, (Mathematics)
    • May 2016
      Ahmed Ali, (Mathematics)
    • Aug 2013
      Weichao Wang, (Mathematics)
    • May 2013
      Charles Garrett, (Mathematics)

Courses

      • MATH 6699-007 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2020
      • MATH 6311-001 OPTIMIZATION ON BIG DATA
        (Course Id: 113156)
        Spring - Regular Academic Session - 2020
      • MATH 5999-003 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Spring - Regular Academic Session - 2020
      • MATH 6399-004 DISSERTATION
        (Course Id: 110859)
        Fall - Regular Academic Session - 2019
      • MATH 6310-001 FOUNDATION OF DATA SCIENCES
        (Course Id: 113183)
        Fall - Regular Academic Session - 2019
      • MATH 5699-003 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2019
      • MATH 5699-002 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2019
      • MATH 2425-050 CALCULUS II
        (Course Id: 108353)
        Spring - Regular Academic Session - 2019
      • MATH 2425-051 CALCULUS II
        (Course Id: 108353)
        Spring - Regular Academic Session - 2019
      • MATH 2425-052 CALCULUS II
        (Course Id: 108353)
        Spring - Regular Academic Session - 2019
      • MATH 7399-002 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Spring - Regular Academic Session - 2019
      • MATH 5399-004 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2019
      • MATH 5999-002 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Spring - Regular Academic Session - 2019
      • MATH 6699-006 DISSERTATION
        (Course Id: 110860)
        Fall - Regular Academic Session - 2018
      • MATH 6310-001 FOUNDATION OF DATA SCIENCES
        (Course Id: 113183)
        Fall - Regular Academic Session - 2018
      • MATH 5391-004 SPECIAL TOPICS IN MATH
        (Course Id: 108486)
        Fall - Regular Academic Session - 2018
      • MATH 7399-002 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Summer - Eleven Week - 2018
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Summer - Eleven Week - 2018
      • MATH 5699-001 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2018
      • MATH 3335-001 ANALYSIS I
        (Course Id: 108373)
        Spring - Regular Academic Session - 2018 Download Syllabus
      • MATH 6699-003 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2018
      • MATH 5399-004 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2018
      • MATH 5999-007 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Spring - Regular Academic Session - 2018
      • MATH 2425-400 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2017
      • MATH 2425-401 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2017
      • MATH 2425-402 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2017
      • MATH 2425-403 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2017 Download Syllabus
      • MATH 6699-001 DISSERTATION
        (Course Id: 110860)
        Fall - Regular Academic Session - 2017
      • MATH 5399-003 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2017
      • MATH 5699-003 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2017
      • MATH 5999-001 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Fall - Regular Academic Session - 2017
      • MATH 6699-002 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2017
      • MATH 7399-005 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Summer - Eleven Week - 2017
      • MATH 5699-005 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2017
      • MATH 6699-003 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2017
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402)
        Spring - Regular Academic Session - 2017 Download Syllabus
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2017 Download Syllabus
      • MATH 5699-003 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2017
      • MATH 5999-003 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Spring - Regular Academic Session - 2017
      • MATH 6999-001 DISSERTATION
        (Course Id: 110861)
        Fall - Regular Academic Session - 2016
      • MATH 7399-001 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Fall - Regular Academic Session - 2016
      • MATH 4322-001 INTRO COMPLEX VARIABLES
        (Course Id: 108393)
        Fall - Regular Academic Session - 2016 Download Syllabus
      • MATH 5699-008 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2016
      • MATH 6399-001 DISSERTATION
        (Course Id: 110859)
        Summer - Eleven Week - 2016
      • MATH 6699-008 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2016
      • MATH 5699-006 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2016
      • MATH 6699-009 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2016
      • MATH 6999-001 DISSERTATION
        (Course Id: 110861)
        Spring - Regular Academic Session - 2016
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2016
      • MATH 5699-002 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2016
      • MATH 5392-003 SELECTED TOPICS IN MATH
        (Course Id: 108487)
        Spring - Regular Academic Session - 2016 Download Syllabus
      • MATH 6399-003 DISSERTATION
        (Course Id: 110859)
        Fall - Regular Academic Session - 2015
      • MATH 5399-003 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2015
      • MATH 5699-004 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2015
      • MATH 5392-006 SELECTED TOPICS IN MATH
        (Topic: Matrix Techniques | Course Id: 108487)
        Fall - Regular Academic Session - 2015 Download Syllabus
      • MATH 6699-001 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2015
      • MATH 5399-001 RESEARCH IN MATHEMATICS
        (Topic: Random Networks | Course Id: 112022)
        Summer - Eleven Week - 2015
      • MATH 5699-004 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2015
      • MATH 5308-001 MATHEMATICAL ANALYSIS II
        (Course Id: 108422)
        Spring - Regular Academic Session - 2015 Download Syllabus
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2015
      • MATH 5699-005 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2015
      • MATH 5999-004 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Spring - Regular Academic Session - 2015
      • MATH 5307-001 MATHEMATICAL ANALYSIS I
        (Course Id: 108421)
        Fall - Regular Academic Session - 2014 Download Syllabus
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Fall - Regular Academic Session - 2014
      • MATH 5699-003 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2014
      • MATH 5999-002 RESEARCH IN MATHEMATICS
        (Course Id: 112024)
        Fall - Regular Academic Session - 2014
      • MATH 5399-002 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Summer - Eleven Week - 2014
      • MATH 5699-002 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Summer - Eleven Week - 2014
      • MATH 5371-001 APPLIED NUM. LINEAR ALGEBRA
        (Course Id: 108481)
        Spring - Regular Academic Session - 2014 Download Syllabus
      • MATH 5399-001 RESEARCH IN MATHEMATICS
        (Course Id: 112022)
        Spring - Regular Academic Session - 2014
      • MATH 5699-002 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Spring - Regular Academic Session - 2014
      • MATH 5699-001 RESEARCH IN MATHEMATICS
        (Course Id: 112023)
        Fall - Regular Academic Session - 2013
      • MATH 7399-003 DOCTORAL DEGREE COMPLETION
        (Course Id: 111647)
        Summer - Eleven Week - 2013
      • MATH 6699-009 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2013
      • MATH 6999-004 DISSERTATION
        (Course Id: 110861)
        Spring - Regular Academic Session - 2013
      • HONR-SC 2425-100 HONORS CALCULUS II
        (Course Id: 103845)
        Spring - Regular Academic Session - 2013 Download Syllabus
      • MATH 5395-006 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2013
      • MATH 5391-016 SPECIAL TOPICS IN MATH
        (Topic: Topics in Medical Imaging | Course Id: 108486)
        Spring - Regular Academic Session - 2013
      • MATH 5371-001 APPLIED NUM. LINEAR ALGEBRA
        (Course Id: 108481)
        Fall - Regular Academic Session - 2012 Download Syllabus
      • MATH 6999-002 DISSERTATION
        (Course Id: 110861)
        Fall - Regular Academic Session - 2012
      • MATH 6699-006 DISSERTATION
        (Course Id: 110860)
        Summer - Eleven Week - 2012
      • MATH 6999-002 DISSERTATION
        (Course Id: 110861)
        Spring - Regular Academic Session - 2012
      • MATH 4345-001 NUM ANLYS & CMPTR APPS II
        (Course Id: 108402)
        Spring - Regular Academic Session - 2012 Download Syllabus
      • MATH 5339-001 NUMERICAL ANALYSIS II
        (Course Id: 108453)
        Spring - Regular Academic Session - 2012 Download Syllabus
      • MATH 5395-010 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2012
      • MATH 2326-002 CALCULUS III
        (Course Id: 108349)
        Fall - Regular Academic Session - 2011
      • MATH 6399-003 DISSERTATION
        (Course Id: 110859)
        Fall - Regular Academic Session - 2011
      • MATH 5338-001 NUMERICAL ANALYSIS I
        (Course Id: 108452)
        Fall - Regular Academic Session - 2011
      • MATH 4391-001 SPECIAL TOPICS IN MATH
        (Course Id: 108404)
        Fall - Regular Academic Session - 2011
      • MATH 6699-001 DISSERTATION
        (Course Id: 110860)
        Summer - Five Week - Second - 2011
      • MATH 5371-001 APPLIED NUM. LINEAR ALGEBRA
        (Course Id: 108481)
        Spring - Regular Academic Session - 2011
      • MATH 6699-004 DISSERTATION
        (Course Id: 110860)
        Spring - Regular Academic Session - 2011
      • MATH 5395-002 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2011
      • MATH 1426-005 CALCULUS I
        (Course Id: 108344)
        Fall - Regular Academic Session - 2010
      • MATH 5392-006 SELECTED TOPICS IN MATH
        (Topic: Sparse Matrix Computations | Course Id: 108487)
        Fall - Regular Academic Session - 2010
      • MATH 5391-003 SPECIAL TOPICS IN MATH
        (Topic: Numerical Computation | Course Id: 108486)
        Summer - Eleven Week - 2010
      • MATH 3330-001 MATRICES & LINEAR ALGEBRA
        (Course Id: 108372)
        Spring - Regular Academic Session - 2010
      • MATH 5392-007 SELECTED TOPICS IN MATH
        (Topic: Num Linear Algbr & Data Mining | Course Id: 108487)
        Spring - Regular Academic Session - 2010
      • MATH 5395-002 SPECIAL PROJECT
        (Course Id: 108489)
        Spring - Regular Academic Session - 2010
      • MATH 5371-001 APPLIED NUM. LINEAR ALGEBRA
        (Course Id: 108481)
        Fall - Regular Academic Session - 2009
      • MATH 2425-001 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2009
      • MATH 2425-101 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2009
      • MATH 2425-201 CALCULUS II
        (Course Id: 108353)
        Fall - Regular Academic Session - 2009

Service to the University

    • June 2019 to  Present Committee Chair
      Mathematics Hiring Committee
    • Aug 2016 to  Present Program Coordinator
      Mathematics Colloquium
    • Apr 2007 to  Present Program Coordinator
      Mathematics Technical Report
    • Sept 2006 to  Present Program Organizer
      Applied Mathematics Seminar Coordinator
    • Sept 2006 to  Present Mathematics Representative
      UTA Library
    • June 2016 to  May 2019 Committee Member
      College of Science Award Committee
    • June 2017 to  Apr 2019 Committee Member
      Mathematics Award Committee
    • Sept 2017 to  May 2018 Committee Member
      College of Science Hiring Committee
    • June 2015 to  Apr 2017 Committee Member
      Chair's Advisory Committee
    • June 2014 to  Apr 2015 Committee Member
      Mathematics Graduate Advising Committee
    • June 2013 to  May 2014 Committee Chair
      Mathematics Graduate Advising Committee
    • June 2012 to  Apr 2014 Committee Member
      Mathematics Undergraduate Advising Committee
    • June 2011 to  Apr 2012 Committee Chair
      Mathematics Award Committee
    • June 2011 to  Apr 2012 Committee Member
      Mathematics Hiring Committee
    • June 2007 to  Apr 2008 Committee Chair
      Mathematics Award Committee

Service to the Profession

    • Jan 2019 to  Present
      Editor, Associate Editor
      Results in Applied Mathematics
    • Dec 2017 to  Present
      Editor, Associate Editor
      Mathematical Communications
    • May 2013 to  Present
      Editor, Journal Editor
      Journal of Mathematical Study
    • Oct 2012 to  Present
      Editor, Journal Editor
      Linear and Multilinear Algebra
    • Dec 2011 to  Sept 2018
      Editor, Journal Editor
      Operators and Matrices
    • Jan 2011 to  Sept 2017
      Editor, Associate Editor
      Numerical Algebra, Control and Optimization
    • Dec 2006 to  Dec 2012
      Editor, Associate Editor
      SIAM Journal on Matrix Analysis and Applications