Edit Profile (opens in new tab) Li, Rencang Compute Distance To: Compute Author ID: li.rencang Published as: Li, Ren-Cang; Li, Rencang; Li, RenCang; Li, Ren-cang more...less Documents Indexed: 129 Publications since 1988, including 1 Book Co-Authors: 65 Co-Authors with 86 Joint Publications 1,892 Co-Co-Authors all top 5 Co-Authors 36 single-authored 14 Zhang, Lei-Hong 12 Bai, Zhaojun 8 Truhar, Ninoslav 7 Lu, Linzhang 7 Xue, Jungong 5 Bhatia, Rajendra 5 Wang, Weiguo 5 Xu, Shufang 5 Ye, Qiang 4 Liang, Xin 4 Lin, Wen-Wei 4 Liu, Changli 4 Teng, Zhongming 4 Wang, Li 3 Huang, Tsungming 3 Kahan, William Morton 3 Nakatsukasa, Yuji 3 Shen, Chungen 2 Cai, Yunfeng 2 Garrett, C. Kristopher 2 Kittaneh, Fuad 2 Li, Chi-Kwong 2 Lin, Wenwei 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 Higham, Nicholas J. 1 Hoffnung, Leonard 1 Huang, Weiqiang 1 Imakura, Akira 1 Karaduman, Gül 1 Kuo, Yueh-Cheng 1 Lee, Cherung 1 Li, Tiexiang 1 Li, Wang 1 Li, Xing 1 Lu, Ding 1 Ma, Changfeng 1 Ma, Xijun 1 Overton, Michael L. 1 Salling, K. B. 1 Shao, Rongxia 1 Stewart, Gilbert Wright 1 Su, Yangfeng 1 Tisseur, Françoise 1 Wang, Chern-Shuh 1 Wang, Teng 1 Wang, Xiang 1 Wei, Tingting 1 Xie, Jinjun 1 Yang, Weihong 1 Zha, Hongyuan 1 Zhang, Shao-Liang 1 Zhu, Hui June all top 5 Serials 27 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 3 Linear and Multilinear Algebra 3 Science China. Mathematics 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 The ANZIAM Journal 2 Communications in Mathematical Sciences 2 Numerical Algebra, Control and Optimization 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Acta Mechanica 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 European Journal of Operational Research 1 SIAM Review 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 97 Numerical analysis (65-XX) 81 Linear and multilinear algebra; matrix theory (15-XX) 10 Operations research, mathematical programming (90-XX) 7 Systems theory; control (93-XX) 6 Operator theory (47-XX) 4 Ordinary differential equations (34-XX) 3 Quantum theory (81-XX) 2 Statistics (62-XX) 2 Computer science (68-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 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 110 Publications have been cited 1,007 times in 595 Documents Cited by ▼ Year ▼ On the ADI method for Sylvester equations. Zbl 1176.65050Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 75 2009 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010Li, Ren-Cang 48 1998 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 42 2008 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009Li, Ren-Cang 37 1998 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102Bai, Zhaojun; Li, Ren-Cang 29 2013 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 28 2012 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078Bai, Zhaojun; Li, Ren-Cang 27 2012 Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060Kahan, William; Li, Ren-Cang 26 1997 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025Xue, Jungong; Xu, Shufang; Li, Ren-Cang 24 2012 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027Li, Chi-Kwong; Li, Ren-Cang 24 2005 New perturbation bounds for the unitary polar factor. Zbl 0817.15012Li, Ren-Cang 22 1995 A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038Li, Ren-Cang; Ye, Qiang 20 2003 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028Li, Ren-Cang; Bai, Zhaojun 18 2005 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008Li, Ren-Cang 18 2003 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007Li, Ren-Cang 17 1993 Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128Zhang, LeiHong; Li, RenCang 17 2014 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 17 2018 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073Li, Ren-Cang; Zhang, Lei-Hong 16 2015 On perturbations of matrix pencils with real spectra. Zbl 0795.15012Li, Ren-Cang 14 1994 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102Zhang, Leihong; Li, Rencang 14 2015 Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022Zhou, Yunkai; Li, Ren-Cang 14 2011 A perturbation bound for definite pencils. Zbl 0813.15017Li, Ren-Cang 13 1993 Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011Li, Ren-Cang 13 1997 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 13 2006 A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang 12 1996 Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. Zbl 0770.15009Li, Rencang 12 1993 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053Xue, Jungong; Xu, Shufang; Li, Ren-Cang 12 2012 Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018Li, Ren-Cang 12 1997 On the generalized Lanczos trust-region method. Zbl 1380.90210Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 12 2017 On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027Li, Ren-Cang 11 2008 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 10 2013 Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040Teng, Zhongming; Li, Ren-Cang 10 2013 Bounds on perturbations of generalized singular values and of associated subspaces. Zbl 0771.15002Li, Ren-Cang 9 1993 On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008Bhatia, Rajendra; Li, Ren-Cang 9 1996 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038Chang, Xiao-Wen; Li, Ren-Cang 9 2011 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053Bai, Zhaojun; Li, Ren-Cang 9 2014 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018Li, Ren-Cang 9 1999 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 9 2020 On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006Li, Rencang 8 1992 Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh 8 2010 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021Bai, ZhaoJun; Li, RenCang; Lin, WenWei 8 2016 An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem. Zbl 1418.90265Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang 8 2019 Pinchings and norms of scaled triangular matrices. Zbl 1004.15020Bhatia, Rajendra; Kahan, William; Li, Ren-Cang 7 2002 QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527Li, Rencang 7 1989 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053Li, Ren-Cang 7 2015 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049Xue, Jungong; Li, Ren-Cang 7 2017 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 7 2011 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 7 1997 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132Li, Ren-Cang 6 2010 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033Liang, Xin; Li, Ren-Cang 6 2015 Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 6 2015 A new relative perturbation theorem for singular subspaces. Zbl 0962.15012Li, Ren-Cang; Stewart, G. W. 6 2000 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 6 2016 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025Li, Ren-Cang 6 2008 Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang 5 2014 Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem. Zbl 1350.65081Zhang, 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 1363.65097Lu, Linzhang; Yuan, Fei; Li, Ren-Cang 5 2015 Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. Zbl 1193.65045Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang 5 2010 A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080Li, Ren-Cang; Kahan, William 5 2012 A Krylov subspace method for large-scale second-order cone linear complementarity problem. Zbl 1326.90090Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang 5 2015 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016Li, Ren-Cang; Zhang, Wei 5 2009 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 5 2016 Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026Shi, Y. J.; Li, R.; Wei, T. T. 5 2015 Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036Li, Ren-Cang 5 2004 Spectral variations and Hadamard products: Some problems. Zbl 0933.15032Li, Ren-Cang 5 1998 A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei 5 2017 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011Li, Ren-Cang 5 2006 Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020Li, Ren-Cang 5 2007 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017Li, Ren-Cang 4 2000 Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010Li, Ren-Cang 4 2005 Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang 4 2007 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 4 2019 A fast algorithm for fast train palindromic quadratic eigenvalue problems. Zbl 1352.65121Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei 4 2016 Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang 4 2007 On the variation of the spectra of matrix pencils. Zbl 0709.15010Li, Rencang 4 1990 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 4 2013 A new two-phase structure-preserving doubling algorithm for critically singular \(M\)-matrix algebraic Riccati equations. Zbl 1374.65068Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei 4 2016 Algorithms for inverse eigenvalue problems. Zbl 0751.65027Li, Rencang 3 1992 A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028Truhar, Ninoslav; Li, Ren-Cang 3 2003 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033Li, Ren-Cang; Zhang, Wei 3 2009 Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071Li, Ren-Cang; Ye, Qiang 3 2014 Monotonicity of unitarily invariant norms. Zbl 1303.15029Wang, Xue-Feng; Li, Ren-Cang 3 2015 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 3 2018 An interpolating family of means. Zbl 1331.26053Bhatia, Rajendra; Li, Ren-Cang 3 2012 Eigenvalues of symmetrizable matrices. Zbl 0898.15015Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 3 1998 Hard cases for conjugate gradient method. Zbl 1156.65031Li, Ren-Cang 3 2008 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 3 2016 A converse to the Bauer-Fike type theorem. Zbl 0655.15011Li, Rencang 3 1988 Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291Wen, M.; Li, R.; Salling, K. B. 3 2016 Solution of linear matrix equation \(AXD-BXC=S\) and perturbation of eigenspaces of a matrix pencil. Zbl 0793.15010Li, Rencang 2 1992 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015Liang, Xin; Li, Ren-Cang 2 2014 The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048Croot, Ernie; Li, Ren-Cang; Zhu, Hui June 2 2004 On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504Li, Rencang 2 1989 Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008Li, Ren-Cang 2 2006 Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011Li, Rencang 2 1989 Optimal parameters for doubling algorithms. Zbl 1413.65138Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang 2 2017 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 2 2008 Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations. Zbl 1445.65012Liu, Changli; Xue, Jungong; Li, Ren-Cang 2 2020 Rotary enclosing control of second-order multi-agent systems for a group of targets. Zbl 1358.93017Shi, Y. J.; Li, R.; Teo, K. L. 2 2017 Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142Bai, Zhaojun; Li, Ren-Cang; Lu, Ding 2 2022 A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction. Zbl 1490.90213Ma, Xijun; Shen, Chungen; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang 1 2022 Accurate numerical solution for structured \(M\)-matrix algebraic Riccati equations. Zbl 1470.65068Liu, Changli; Wang, Wei-Guo; Xue, Jungong; Li, Ren-Cang 2 2021 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 9 2020 Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations. Zbl 1445.65012Liu, Changli; Xue, Jungong; Li, Ren-Cang 2 2020 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 2 2020 An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem. Zbl 1418.90265Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang 8 2019 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 4 2019 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 17 2018 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 3 2018 On the generalized Lanczos trust-region method. Zbl 1380.90210Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 12 2017 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049Xue, Jungong; Li, Ren-Cang 7 2017 A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei 5 2017 Optimal parameters for doubling algorithms. Zbl 1413.65138Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang 2 2017 Rotary enclosing control of second-order multi-agent systems for a group of targets. Zbl 1358.93017Shi, Y. J.; Li, R.; Teo, K. L. 2 2017 Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang 1 2017 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021Bai, ZhaoJun; Li, RenCang; Lin, WenWei 8 2016 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 6 2016 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 5 2016 A fast algorithm for fast train palindromic quadratic eigenvalue problems. Zbl 1352.65121Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei 4 2016 A new two-phase structure-preserving doubling algorithm for critically singular \(M\)-matrix algebraic Riccati equations. Zbl 1374.65068Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei 4 2016 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 3 2016 Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291Wen, M.; Li, R.; Salling, K. B. 3 2016 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073Li, Ren-Cang; Zhang, Lei-Hong 16 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102Zhang, Leihong; Li, Rencang 14 2015 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053Li, Ren-Cang 7 2015 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033Liang, Xin; Li, Ren-Cang 6 2015 Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 6 2015 Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem. Zbl 1350.65081Zhang, 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 1363.65097Lu, Linzhang; Yuan, Fei; Li, Ren-Cang 5 2015 A Krylov subspace method for large-scale second-order cone linear complementarity problem. Zbl 1326.90090Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang 5 2015 Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026Shi, Y. J.; Li, R.; Wei, T. T. 5 2015 Monotonicity of unitarily invariant norms. Zbl 1303.15029Wang, Xue-Feng; Li, Ren-Cang 3 2015 Perturbation of partitioned linear response eigenvalue problems. Zbl 1330.65060Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 1 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128Zhang, LeiHong; Li, RenCang 17 2014 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053Bai, Zhaojun; Li, Ren-Cang 9 2014 Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang 5 2014 Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071Li, Ren-Cang; Ye, Qiang 3 2014 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015Liang, Xin; Li, Ren-Cang 2 2014 Dynamic viscoelastic modeling of magnetorheological elastomers. Zbl 1401.74055Li, R.; Sun, L. Z. 1 2014 GIP integrators for matrix Riccati differential equations. Zbl 1337.65074Kristopher Garrett, C.; Li, Ren-Cang 1 2014 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102Bai, Zhaojun; Li, Ren-Cang 29 2013 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 10 2013 Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040Teng, Zhongming; Li, Ren-Cang 10 2013 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 4 2013 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 28 2012 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078Bai, Zhaojun; Li, Ren-Cang 27 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025Xue, Jungong; Xu, Shufang; Li, Ren-Cang 24 2012 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053Xue, Jungong; Xu, Shufang; Li, Ren-Cang 12 2012 A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080Li, Ren-Cang; Kahan, William 5 2012 An interpolating family of means. Zbl 1331.26053Bhatia, Rajendra; Li, Ren-Cang 3 2012 Perturbation of multiple eigenvalues of Hermitian matrices. Zbl 1242.15016Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Wang, Wei-Guo 1 2012 Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022Zhou, Yunkai; Li, Ren-Cang 14 2011 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038Chang, Xiao-Wen; Li, Ren-Cang 9 2011 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 7 2011 Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang 1 2011 Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh 8 2010 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132Li, Ren-Cang 6 2010 Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. Zbl 1193.65045Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang 5 2010 On the ADI method for Sylvester equations. Zbl 1176.65050Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 75 2009 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016Li, Ren-Cang; Zhang, Wei 5 2009 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033Li, Ren-Cang; Zhang, Wei 3 2009 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 42 2008 On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027Li, Ren-Cang 11 2008 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025Li, Ren-Cang 6 2008 Hard cases for conjugate gradient method. Zbl 1156.65031Li, Ren-Cang 3 2008 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 2 2008 Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020Li, Ren-Cang 5 2007 Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang 4 2007 Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang 4 2007 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 13 2006 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011Li, Ren-Cang 5 2006 Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008Li, Ren-Cang 2 2006 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027Li, Chi-Kwong; Li, Ren-Cang 24 2005 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028Li, Ren-Cang; Bai, Zhaojun 18 2005 Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010Li, Ren-Cang 4 2005 Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036Li, Ren-Cang 5 2004 The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048Croot, 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 1050.65038Li, Ren-Cang; Ye, Qiang 20 2003 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008Li, Ren-Cang 18 2003 A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028Truhar, Ninoslav; Li, Ren-Cang 3 2003 Pinchings and norms of scaled triangular matrices. Zbl 1004.15020Bhatia, Rajendra; Kahan, William; Li, Ren-Cang 7 2002 A new relative perturbation theorem for singular subspaces. Zbl 0962.15012Li, Ren-Cang; Stewart, G. W. 6 2000 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017Li, Ren-Cang 4 2000 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018Li, Ren-Cang 9 1999 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010Li, Ren-Cang 48 1998 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009Li, Ren-Cang 37 1998 Spectral variations and Hadamard products: Some problems. Zbl 0933.15032Li, Ren-Cang 5 1998 Eigenvalues of symmetrizable matrices. Zbl 0898.15015Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 3 1998 Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060Kahan, William; Li, Ren-Cang 26 1997 Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011Li, Ren-Cang 13 1997 Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018Li, Ren-Cang 12 1997 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 7 1997 A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang 12 1996 On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008Bhatia, Rajendra; Li, Ren-Cang 9 1996 New perturbation bounds for the unitary polar factor. Zbl 0817.15012Li, Ren-Cang 22 1995 On perturbations of matrix pencils with real spectra. Zbl 0795.15012Li, Ren-Cang 14 1994 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007Li, Ren-Cang 17 1993 A perturbation bound for definite pencils. Zbl 0813.15017Li, Ren-Cang 13 1993 ...and 10 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 764 Authors 66 Li, Rencang 22 Zhang, Lei-Hong 21 Benner, Peter 15 Truhar, Ninoslav 12 Dopico, Froilán M. 12 Li, Hanyu 12 Shen, Chungen 11 Bai, Zhaojun 11 Li, Wen 10 Reichel, Lothar 9 Lin, Wen-Wei 9 Nakatsukasa, Yuji 9 Wang, Xiang 9 Ye, Qiang 8 Chen, Xiaoshan 8 Kressner, Daniel 8 Kürschner, Patrick 8 Ma, Changfeng 8 Wei, Yimin 7 Yang, Weihong 6 Blanes, Sergio 6 Chen, Xiaoping 6 Dai, Hua 6 Kittaneh, Fuad 6 Lawrence, Piers W. 6 Liang, Xin 6 Saak, Jens 6 Su, Yangfeng 6 Tisseur, Françoise 6 Townsend, Alex 6 Wei, Wei 6 Yang, Hu 6 Zheng, Bing 5 Bhatia, Rajendra 5 Chen, Hongjia 5 Meng, Lingsheng 5 Saad, Yousef 5 Simoncini, Valeria 5 Slapničar, Ivan 5 Teng, Zhongming 5 Wang, Weiguo 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 Guo, Chun-Hua 4 Huang, Rong 4 Huang, Tsungming 4 Ipsen, Ilse C. F. 4 Li, Jicheng 4 Li, Tiexiang 4 Lu, Ding 4 Lu, Linzhang 4 Miodragović, Suzana 4 Rehman, Abdur 4 Tomljanović, Zoran 4 Wang, Li 4 Wang, Qingwen 4 Wen, Zaiwen 4 Xu, Qingxiang 3 Beckermann, Bernhard 3 Chen, Cairong 3 Chu, Delin 3 Corless, Robert Malcolm 3 Dong, Liqiang 3 Dong, Ning 3 Doostaki, Reza 3 Du, Lei 3 Farooq, Aamir 3 Fu, Chunhong 3 Furtado, Susana 3 Grubišić, Luka 3 Hochstenbach, Michiel E. 3 Huang, Na 3 Huang, Weiqiang 3 Imakura, Akira 3 Jarlebring, Elias 3 Jbilou, Khalide 3 Jia, Lu 3 Jia, Zhongxiao 3 Khoromskiĭ, Boris Nikolaevich 3 Kuo, Yueh-Cheng 3 Kyrchei, Ivan I. 3 Li, Chi-Kwong 3 Li, Yung-Ta 3 Liu, Changli 3 Massey, Pedro G. 3 Meini, Beatrice 3 Molera, Juan M. 3 Palitta, Davide 3 Pandur, Marija Miloloža 3 Parlett, Beresford Neill 3 Pérez, Javier J. 3 Plešinger, Martin 3 Safique Ahmad, Sk. 3 Samar, Mahvish 3 Shao, Meiyue ...and 664 more Authors all top 5 Cited in 150 Serials 91 Linear Algebra and its Applications 36 SIAM Journal on Matrix Analysis and Applications 27 Journal of Computational and Applied Mathematics 24 Numerische Mathematik 24 SIAM Journal on Scientific Computing 22 BIT 21 Linear and Multilinear Algebra 19 Applied Mathematics and Computation 16 Numerical Algorithms 14 Mathematics of Computation 14 Applied Numerical Mathematics 13 Numerical Linear Algebra with Applications 12 Journal of Scientific Computing 11 Computers & Mathematics with Applications 10 Journal of Computational Physics 9 International Journal of Computer Mathematics 8 Calcolo 8 SIAM Journal on Optimization 7 East Asian Journal on Applied Mathematics 6 ETNA. 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Series A 1 Annals of Operations Research 1 Applications of Mathematics 1 Aequationes Mathematicae 1 Glasnik Matematički. Serija III 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 Journal of Mathematical Imaging and Vision 1 Algebra Colloquium 1 Journal of Computational Neuroscience 1 Bernoulli 1 The Journal of Fourier Analysis and Applications 1 Mathematical Problems in Engineering 1 Nonlinear Dynamics 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Mathematical and Computer Modelling of Dynamical Systems 1 Discrete Dynamics in Nature and Society 1 Mathematical & Computational Applications 1 Journal of Mathematical Study ...and 50 more Serials all top 5 Cited in 37 Fields 435 Numerical analysis (65-XX) 337 Linear and multilinear algebra; matrix theory (15-XX) 51 Operations research, mathematical programming (90-XX) 44 Operator theory (47-XX) 33 Systems theory; control (93-XX) 22 Ordinary differential equations (34-XX) 21 Partial differential equations (35-XX) 18 Computer science (68-XX) 12 Dynamical systems and ergodic theory (37-XX) 11 Probability theory and stochastic processes (60-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Mechanics of particles and systems (70-XX) 8 Functions of a complex variable (30-XX) 8 Fluid mechanics (76-XX) 8 Quantum theory (81-XX) 6 Real functions (26-XX) 6 Approximations and expansions (41-XX) 6 Biology and other natural sciences (92-XX) 5 Mechanics of deformable solids (74-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Information and communication theory, circuits (94-XX) 4 Combinatorics (05-XX) 4 Special functions (33-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Statistics (62-XX) 3 Difference and functional equations (39-XX) 2 Number theory (11-XX) 2 Nonassociative rings and algebras (17-XX) 2 Functional analysis (46-XX) 2 General topology (54-XX) 2 Optics, electromagnetic theory (78-XX) 2 Astronomy and astrophysics (85-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Geophysics (86-XX) Citations by Year