Edit Profile (opens in new tab) Li, Rencang Co-Author Distance Author ID: li.rencang Published as: Li, Ren-Cang; Li, Rencang; Li, RenCang; Li, Ren-cang more...less Documents Indexed: 135 Publications since 1988, including 1 Book and 9 Additional arXiv Preprints Co-Authors: 67 Co-Authors with 97 Joint Publications 2,110 Co-Co-Authors all top 5 Co-Authors 37 single-authored 18 Zhang, Lei-Hong 14 Bai, Zhaojun 9 Wang, Li 8 Truhar, Ninoslav 7 Liang, Xin 7 Lu, Linzhang 7 Xue, Jungong 5 Bhatia, Rajendra 5 Huang, Tsungming 5 Teng, Zhongming 5 Wang, Weiguo 5 Xu, Shufang 5 Ye, Qiang 4 Lin, Wen-Wei 4 Liu, Changli 4 Shen, Chungen 3 Kahan, William Morton 3 Kuo, Yueh-Cheng 3 Nakatsukasa, Yuji 2 Cai, Yunfeng 2 Garrett, C. Kristopher 2 Kittaneh, Fuad 2 Li, Chi-Kwong 2 Lin, Wenwei 2 Lu, Ding 2 Tomljanović, Zoran 2 Wang, Weichao 2 Yang, Mei 2 Yuan, Fei 2 Zhang, Wei 2 Zhou, Yunkai 1 Benner, Peter 1 Boldo, Sylvie 1 Cao, Zhihao 1 Chang, Xiaowen 1 Chen, Cairong 1 Croot, Ernie 1 Daumas, Marc 1 Greenbaum, Anne 1 Gu, Guiding 1 Guan, Jinrui 1 Guo, Zhen-chen 1 Higham, Nicholas J. 1 Hoffnung, Leonard 1 Huang, Weiqiang 1 Imakura, Akira 1 Karaduman, Gül 1 Lee, Cherung 1 Li, Tiexiang 1 Li, Wang 1 Li, Xing 1 Ma, Changfeng 1 Ma, Xijun 1 Overton, Michael L. 1 Shao, Rongxia 1 Stewart, Gilbert Wright 1 Su, Yangfeng 1 Tisseur, Françoise 1 Wang, Chern-Shuh 1 Wang, Teng 1 Wang, Xiang 1 Xie, Jinjun 1 Yang, Weihong 1 Zha, Hongyuan 1 Zhang, Shao-Liang 1 Zhou, Yunshen 1 Zhu, Hui June all top 5 Serials 28 Linear Algebra and its Applications 17 SIAM Journal on Matrix Analysis and Applications 8 Mathematics of Computation 8 BIT 7 Numerische Mathematik 5 Journal of Computational and Applied Mathematics 4 Mathematica Numerica Sinica 4 Journal of Computational Mathematics 4 Science China. Mathematics 3 Linear and Multilinear Algebra 2 Applied Mathematics and Computation 2 Journal of Scientific Computing 2 Japan Journal of Industrial and Applied Mathematics 2 SIAM Journal on Scientific Computing 2 Numerical Linear Algebra with Applications 2 Advances in Computational Mathematics 2 Journal of Mathematical Study 2 Communications in Mathematical Sciences 2 Numerical Algebra, Control and Optimization 1 ACM Transactions on Mathematical Software 1 IEEE Transactions on Computers 1 Theoretical Computer Science 1 Systems & Control Letters 1 Journal of Xiamen University. Natural Science 1 SIAM Review 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 ETNA. Electronic Transactions on Numerical Analysis 1 Chinese Journal of Numerical Mathematics and Applications 1 Optimization Methods & Software 1 International Journal of Information & Systems Sciences 1 Frontiers of Mathematics in China 1 Communications on Stochastic Analysis 1 Forum of Mathematics, Sigma 1 Communications in Mathematics and Statistics 1 Annals of Mathematical Sciences and Applications 1 Fundamentals of Algorithms all top 5 Fields 103 Numerical analysis (65-XX) 85 Linear and multilinear algebra; matrix theory (15-XX) 11 Operations research, mathematical programming (90-XX) 6 Operator theory (47-XX) 4 Ordinary differential equations (34-XX) 3 Statistics (62-XX) 3 Quantum theory (81-XX) 3 Systems theory; control (93-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 110 Publications have been cited 1,140 times in 674 Documents Cited by ▼ Year ▼ On the ADI method for Sylvester equations. Zbl 1176.65050 Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 85 2009 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010 Li, Ren-Cang 53 1998 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042 Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 46 2008 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009 Li, Ren-Cang 39 1998 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102 Bai, Zhaojun; Li, Ren-Cang 32 2013 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045 Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 31 2012 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078 Bai, Zhaojun; Li, Ren-Cang 30 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025 Xue, Jungong; Xu, Shufang; Li, Ren-Cang 27 2012 New perturbation bounds for the unitary polar factor. Zbl 0817.15012 Li, Ren-Cang 26 1995 Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060 Kahan, William; Li, Ren-Cang 26 1997 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027 Li, Chi-Kwong; Li, Ren-Cang 24 2005 A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038 Li, Ren-Cang; Ye, Qiang 21 2003 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036 Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 20 2018 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008 Li, Ren-Cang 19 2003 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028 Li, Ren-Cang; Bai, Zhaojun 19 2005 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007 Li, Ren-Cang 18 1993 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073 Li, Ren-Cang; Zhang, Lei-Hong 18 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128 Zhang, LeiHong; Li, RenCang 18 2014 On perturbations of matrix pencils with real spectra. Zbl 0795.15012 Li, Ren-Cang 17 1994 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 1516.15006 Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 17 2020 Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022 Zhou, Yunkai; Li, Ren-Cang 16 2011 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102 Zhang, Leihong; Li, Rencang 15 2015 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032 Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 14 2006 On the generalized Lanczos trust-region method. Zbl 1380.90210 Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 14 2017 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010 Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 14 2013 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053 Xue, Jungong; Xu, Shufang; Li, Ren-Cang 13 2012 A perturbation bound for definite pencils. Zbl 0813.15017 Li, Ren-Cang 13 1993 Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018 Li, Ren-Cang 13 1997 Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011 Li, Ren-Cang 13 1997 Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. Zbl 0770.15009 Li, Rencang 13 1993 A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017 Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang 13 1996 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006 Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 13 2018 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053 Li, Ren-Cang 12 2015 On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027 Li, Ren-Cang 11 2008 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038 Chang, Xiao-Wen; Li, Ren-Cang 11 2011 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053 Bai, Zhaojun; Li, Ren-Cang 11 2014 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018 Li, Ren-Cang 10 1999 Bounds on perturbations of generalized singular values and of associated subspaces. Zbl 0771.15002 Li, Ren-Cang 10 1993 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033 Liang, Xin; Li, Ren-Cang 10 2015 Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040 Teng, Zhongming; Li, Ren-Cang 10 2013 On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008 Bhatia, Rajendra; Li, Ren-Cang 9 1996 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021 Bai, ZhaoJun; Li, RenCang; Lin, WenWei 9 2016 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049 Xue, Jungong; Li, Ren-Cang 9 2017 An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem. Zbl 1418.90265 Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang 9 2019 QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527 Li, Rencang 8 1989 On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006 Li, Rencang 8 1992 Pinchings and norms of scaled triangular matrices. Zbl 1004.15020 Bhatia, Rajendra; Kahan, William; Li, Ren-Cang 8 2002 Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063 Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh 8 2010 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011 Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 7 2011 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012 Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 7 1997 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046 Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 7 2016 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132 Li, Ren-Cang 7 2010 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025 Li, Ren-Cang 6 2008 A new relative perturbation theorem for singular subspaces. Zbl 0962.15012 Li, Ren-Cang; Stewart, G. W. 6 2000 A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080 Li, Ren-Cang; Kahan, William 6 2012 Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036 Li, Ren-Cang 6 2004 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063 Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 6 2016 Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013 Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 6 2015 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011 Li, Ren-Cang 5 2006 Spectral variations and Hadamard products: Some problems. Zbl 0933.15032 Li, Ren-Cang 5 1998 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017 Li, Ren-Cang 5 2000 Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020 Li, Ren-Cang 5 2007 Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010 Li, Ren-Cang 5 2005 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016 Li, Ren-Cang; Zhang, Wei 5 2009 Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126 Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang 5 2014 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015 Liang, Xin; Li, Ren-Cang 5 2014 Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem. Zbl 1350.65081 Zhang, Lei-Hong; Lin, Wen-Wei; Li, Ren-Cang 5 2015 A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. Zbl 1363.65097 Lu, Linzhang; Yuan, Fei; Li, Ren-Cang 5 2015 An interpolating family of means. Zbl 1331.26053 Bhatia, Rajendra; Li, Ren-Cang 5 2012 A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057 Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei 5 2017 A Krylov subspace method for large-scale second-order cone linear complementarity problem. Zbl 1326.90090 Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang 5 2015 Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. Zbl 1193.65045 Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang 5 2010 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022 Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 5 2019 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005 Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 5 2013 Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019 Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang 4 2007 On the variation of the spectra of matrix pencils. Zbl 0709.15010 Li, Rencang 4 1990 Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062 Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang 4 2007 A fast algorithm for fast train palindromic quadratic eigenvalue problems. Zbl 1352.65121 Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei 4 2016 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010 Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 4 2008 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057 Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 4 2016 A new two-phase structure-preserving doubling algorithm for critically singular \(M\)-matrix algebraic Riccati equations. Zbl 1374.65068 Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei 4 2016 Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142 Bai, Zhaojun; Li, Ren-Cang; Lu, Ding 4 2022 Optimal parameters for doubling algorithms. Zbl 1413.65138 Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang 4 2017 A converse to the Bauer-Fike type theorem. Zbl 0655.15011 Li, Rencang 3 1988 Eigenvalues of symmetrizable matrices. Zbl 0898.15015 Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 3 1998 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033 Li, Ren-Cang; Zhang, Wei 3 2009 A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028 Truhar, Ninoslav; Li, Ren-Cang 3 2003 Algorithms for inverse eigenvalue problems. Zbl 0751.65027 Li, Rencang 3 1992 Monotonicity of unitarily invariant norms. Zbl 1303.15029 Wang, Xue-Feng; Li, Ren-Cang 3 2015 Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071 Li, Ren-Cang; Ye, Qiang 3 2014 Hard cases for conjugate gradient method. Zbl 1156.65031 Li, Ren-Cang 3 2008 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059 Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 3 2020 On generalizing trace minimization principles. Zbl 1501.15005 Liang, Xin; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang 3 2023 On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504 Li, Rencang 2 1989 Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008 Li, Ren-Cang 2 2006 Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011 Li, Rencang 2 1989 The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048 Croot, Ernie; Li, Ren-Cang; Zhu, Hui June 2 2004 Solution of linear matrix equation \(AXD-BXC=S\) and perturbation of eigenspaces of a matrix pencil. Zbl 0793.15010 Li, Rencang 2 1992 Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035 Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang 2 2011 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096 Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 On generalizing trace minimization principles. Zbl 1501.15005 Liang, Xin; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang 3 2023 Nearly optimal stochastic approximation for online principal subspace estimation. Zbl 1515.65027 Liang, Xin; Guo, Zhen-Chen; Wang, Li; Li, Ren-Cang; Lin, Wen-Wei 1 2023 Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142 Bai, Zhaojun; Li, Ren-Cang; Lu, Ding 4 2022 A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction. Zbl 1490.90213 Ma, Xijun; Shen, Chungen; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang 1 2022 Accurate numerical solution for structured \(M\)-matrix algebraic Riccati equations. Zbl 1470.65068 Liu, Changli; Wang, Wei-Guo; Xue, Jungong; Li, Ren-Cang 2 2021 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 1516.15006 Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 17 2020 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059 Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 3 2020 Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations. Zbl 1445.65012 Liu, Changli; Xue, Jungong; Li, Ren-Cang 2 2020 Perturbation theory for Hermitian quadratic eigenvalue problem – damped and simultaneously diagonalizable systems. Zbl 1433.15019 Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang 1 2020 An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem. Zbl 1418.90265 Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang 9 2019 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022 Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 5 2019 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036 Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 20 2018 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006 Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 13 2018 On the generalized Lanczos trust-region method. Zbl 1380.90210 Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 14 2017 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049 Xue, Jungong; Li, Ren-Cang 9 2017 A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057 Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei 5 2017 Optimal parameters for doubling algorithms. Zbl 1413.65138 Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang 4 2017 Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016 Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang 1 2017 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021 Bai, ZhaoJun; Li, RenCang; Lin, WenWei 9 2016 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046 Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 7 2016 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063 Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 6 2016 A fast algorithm for fast train palindromic quadratic eigenvalue problems. Zbl 1352.65121 Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei 4 2016 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057 Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 4 2016 A new two-phase structure-preserving doubling algorithm for critically singular \(M\)-matrix algebraic Riccati equations. Zbl 1374.65068 Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei 4 2016 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096 Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073 Li, Ren-Cang; Zhang, Lei-Hong 18 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102 Zhang, Leihong; Li, Rencang 15 2015 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053 Li, Ren-Cang 12 2015 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033 Liang, Xin; Li, Ren-Cang 10 2015 Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013 Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 6 2015 Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem. Zbl 1350.65081 Zhang, Lei-Hong; Lin, Wen-Wei; Li, Ren-Cang 5 2015 A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. Zbl 1363.65097 Lu, Linzhang; Yuan, Fei; Li, Ren-Cang 5 2015 A Krylov subspace method for large-scale second-order cone linear complementarity problem. Zbl 1326.90090 Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang 5 2015 Monotonicity of unitarily invariant norms. Zbl 1303.15029 Wang, Xue-Feng; Li, Ren-Cang 3 2015 Perturbation of partitioned linear response eigenvalue problems. Zbl 1330.65060 Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 1 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128 Zhang, LeiHong; Li, RenCang 18 2014 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053 Bai, Zhaojun; Li, Ren-Cang 11 2014 Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126 Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang 5 2014 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015 Liang, Xin; Li, Ren-Cang 5 2014 Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071 Li, Ren-Cang; Ye, Qiang 3 2014 GIP integrators for matrix Riccati differential equations. Zbl 1337.65074 Kristopher Garrett, C.; Li, Ren-Cang 2 2014 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102 Bai, Zhaojun; Li, Ren-Cang 32 2013 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010 Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 14 2013 Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040 Teng, Zhongming; Li, Ren-Cang 10 2013 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005 Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 5 2013 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045 Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 31 2012 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078 Bai, Zhaojun; Li, Ren-Cang 30 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025 Xue, Jungong; Xu, Shufang; Li, Ren-Cang 27 2012 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053 Xue, Jungong; Xu, Shufang; Li, Ren-Cang 13 2012 A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080 Li, Ren-Cang; Kahan, William 6 2012 An interpolating family of means. Zbl 1331.26053 Bhatia, Rajendra; Li, Ren-Cang 5 2012 Perturbation of multiple eigenvalues of Hermitian matrices. Zbl 1242.15016 Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Wang, Wei-Guo 1 2012 Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022 Zhou, Yunkai; Li, Ren-Cang 16 2011 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038 Chang, Xiao-Wen; Li, Ren-Cang 11 2011 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011 Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 7 2011 Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035 Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang 2 2011 Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063 Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh 8 2010 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132 Li, Ren-Cang 7 2010 Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. Zbl 1193.65045 Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang 5 2010 On the ADI method for Sylvester equations. Zbl 1176.65050 Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 85 2009 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016 Li, Ren-Cang; Zhang, Wei 5 2009 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033 Li, Ren-Cang; Zhang, Wei 3 2009 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042 Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 46 2008 On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027 Li, Ren-Cang 11 2008 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025 Li, Ren-Cang 6 2008 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010 Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 4 2008 Hard cases for conjugate gradient method. Zbl 1156.65031 Li, Ren-Cang 3 2008 Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020 Li, Ren-Cang 5 2007 Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019 Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang 4 2007 Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062 Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang 4 2007 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032 Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 14 2006 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011 Li, Ren-Cang 5 2006 Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008 Li, Ren-Cang 2 2006 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027 Li, Chi-Kwong; Li, Ren-Cang 24 2005 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028 Li, Ren-Cang; Bai, Zhaojun 19 2005 Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010 Li, Ren-Cang 5 2005 Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036 Li, Ren-Cang 6 2004 The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048 Croot, Ernie; Li, Ren-Cang; Zhu, Hui June 2 2004 A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038 Li, Ren-Cang; Ye, Qiang 21 2003 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008 Li, Ren-Cang 19 2003 A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028 Truhar, Ninoslav; Li, Ren-Cang 3 2003 Pinchings and norms of scaled triangular matrices. Zbl 1004.15020 Bhatia, Rajendra; Kahan, William; Li, Ren-Cang 8 2002 A new relative perturbation theorem for singular subspaces. Zbl 0962.15012 Li, Ren-Cang; Stewart, G. W. 6 2000 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017 Li, Ren-Cang 5 2000 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018 Li, Ren-Cang 10 1999 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010 Li, Ren-Cang 53 1998 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009 Li, Ren-Cang 39 1998 Spectral variations and Hadamard products: Some problems. Zbl 0933.15032 Li, Ren-Cang 5 1998 Eigenvalues of symmetrizable matrices. Zbl 0898.15015 Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 3 1998 Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060 Kahan, William; Li, Ren-Cang 26 1997 Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018 Li, Ren-Cang 13 1997 Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011 Li, Ren-Cang 13 1997 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012 Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 7 1997 A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017 Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang 13 1996 On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008 Bhatia, Rajendra; Li, Ren-Cang 9 1996 New perturbation bounds for the unitary polar factor. Zbl 0817.15012 Li, Ren-Cang 26 1995 On perturbations of matrix pencils with real spectra. Zbl 0795.15012 Li, Ren-Cang 17 1994 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007 Li, Ren-Cang 18 1993 A perturbation bound for definite pencils. Zbl 0813.15017 Li, Ren-Cang 13 1993 Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. Zbl 0770.15009 Li, Rencang 13 1993 ...and 10 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 882 Authors 69 Li, Rencang 23 Zhang, Lei-Hong 22 Benner, Peter 17 Li, Wen 16 Truhar, Ninoslav 14 Dopico, Froilán M. 12 Bai, Zhaojun 12 Li, Hanyu 12 Shen, Chungen 10 Liang, Xin 10 Nakatsukasa, Yuji 10 Reichel, Lothar 10 Wang, Xiang 10 Wei, Yimin 9 Kressner, Daniel 9 Lin, Wen-Wei 9 Ma, Changfeng 9 Ye, Qiang 8 Chen, Xiaoshan 8 Kürschner, Patrick 7 Chen, Xiaoping 7 Dai, Hua 7 Saak, Jens 7 Townsend, Alex 7 Yang, Chao 7 Yang, Weihong 6 Blanes, Sergio 6 Chen, Hongjia 6 Kittaneh, Fuad 6 Lawrence, Piers W. 6 Su, Yangfeng 6 Tisseur, Françoise 6 Wang, Weiguo 6 Wei, Wei 6 Yang, Hu 6 Zheng, Bing 5 Bhatia, Rajendra 5 Huang, Tsungming 5 Lu, Ding 5 Meng, Lingsheng 5 Miodragović, Suzana 5 Rehman, Abdur 5 Saad, Yousef 5 Simoncini, Valeria 5 Slapničar, Ivan 5 Stykel, Tatjana 5 Teng, Zhongming 5 Wang, Li 5 Wang, Qingwen 5 Xi, Yuanzhe 5 Xu, Wei-Wei 5 Xue, Jungong 5 Zhou, Yunkai 4 Beik, Fatemeh Panjeh Ali 4 Casas, Fernando 4 de Terán, Fernando 4 Grubišić, Luka 4 Guo, Chun-Hua 4 Guo, Zhen-chen 4 Hochstenbach, Michiel E. 4 Huang, Na 4 Ipsen, Ilse C. F. 4 Jarlebring, Elias 4 Kuo, Yueh-Cheng 4 Kyrchei, Ivan I. 4 Li, Jicheng 4 Li, Tiexiang 4 Lu, Linzhang 4 Palitta, Davide 4 Samar, Mahvish 4 Shao, Meiyue 4 Tomljanović, Zoran 4 Van Dooren, Paul M. 4 Wen, Zaiwen 4 Xu, Qingxiang 3 Beckermann, Bernhard 3 Chen, Cairong 3 Chiang, Chun-Yueh 3 Chu, Delin 3 Corless, Robert Malcolm 3 Cucuringu, Mihai 3 Dolgov, Sergey V. 3 Dong, Liqiang 3 Dong, Ning 3 Doostaki, Reza 3 Drmač, Zlatko 3 Du, Lei 3 Farooq, Aamir 3 Ferreira, Carla 3 Fu, Chunhong 3 Furtado, Susana 3 Huang, Weiqiang 3 Imakura, Akira 3 Jbilou, Khalide 3 Jia, Lu 3 Jia, Zhongxiao 3 Khoromskiĭ, Boris Nikolaevich 3 King-wah Chu, Eric 3 Li, Chi-Kwong 3 Li, Yung-Ta ...and 782 more Authors all top 5 Cited in 165 Serials 97 Linear Algebra and its Applications 44 SIAM Journal on Matrix Analysis and Applications 29 Journal of Computational and Applied Mathematics 26 SIAM Journal on Scientific Computing 25 Numerische Mathematik 24 Linear and Multilinear Algebra 24 BIT 23 Applied Mathematics and Computation 18 Numerical Algorithms 16 Journal of Scientific Computing 15 Applied Numerical Mathematics 14 Mathematics of Computation 13 Numerical Linear Algebra with Applications 12 Computers & Mathematics with Applications 10 Journal of Computational Physics 9 Calcolo 9 International Journal of Computer Mathematics 9 SIAM Journal on Optimization 8 Computational and Applied Mathematics 7 East Asian Journal on Applied Mathematics 6 ETNA. 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Mathematical Sciences 1 Computational Statistics and Data Analysis 1 Journal of Mathematical Imaging and Vision 1 Algebra Colloquium 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Journal of Inverse and Ill-Posed Problems ...and 65 more Serials all top 5 Cited in 39 Fields 491 Numerical analysis (65-XX) 368 Linear and multilinear algebra; matrix theory (15-XX) 60 Operations research, mathematical programming (90-XX) 48 Operator theory (47-XX) 41 Systems theory; control (93-XX) 30 Computer science (68-XX) 25 Partial differential equations (35-XX) 23 Ordinary differential equations (34-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 13 Dynamical systems and ergodic theory (37-XX) 13 Probability theory and stochastic processes (60-XX) 11 Combinatorics (05-XX) 10 Mechanics of particles and systems (70-XX) 10 Fluid mechanics (76-XX) 10 Quantum theory (81-XX) 8 Real functions (26-XX) 8 Functions of a complex variable (30-XX) 8 Information and communication theory, circuits (94-XX) 7 Statistics (62-XX) 6 Special functions (33-XX) 6 Approximations and expansions (41-XX) 6 Mechanics of deformable solids (74-XX) 6 Biology and other natural sciences (92-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Difference and functional equations (39-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Optics, electromagnetic theory (78-XX) 2 Number theory (11-XX) 2 Nonassociative rings and algebras (17-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Astronomy and astrophysics (85-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year