Edit Profile Li, Rencang Compute Distance To: Compute Author ID: li.rencang Published as: Li, R.; Li, Ren-Cang; Li, Ren-cang; Li, RenCang; Li, Rencang Documents Indexed: 126 Publications since 1988, including 1 Book all top 5 Co-Authors 36 single-authored 11 Bai, Zhaojun 11 Zhang, Lei-Hong 8 Lin, Wen-Wei 7 Lu, Linzhang 7 Truhar, Ninoslav 5 Bhatia, Rajendra 5 Xu, Shufang 5 Xue, Jungong 5 Ye, Qiang 4 Teng, Zhongming 4 Wang, Weiguo 3 Huang, Tsungming 3 Kahan, William Morton 3 Liang, Xin 3 Nakatsukasa, Yuji 2 Cai, Yunfeng 2 Garrett, C. Kristopher 2 Kittaneh, Fuad 2 Li, Chi-Kwong 2 Liu, Changli 2 Shen, Chungen 2 Tomljanović, Zoran 2 Wang, Weichao 2 Yuan, Fei 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 Guan, Jinrui 1 Higham, Nicholas J. 1 Hoffnung, Leonard 1 Huang, Weiqiang 1 Imakura, Akira 1 Kuo, Yueh-Cheng 1 Lee, Cherung 1 Li, Tiexiang 1 Li, Xing 1 Ma, Changfeng 1 Overton, Michael L. 1 Shao, Rongxia 1 Stewart, Gilbert Wright 1 Su, Yangfeng 1 Tisseur, Françoise 1 Wang, Chern-Shuh 1 Wang, Li 1 Wang, Teng 1 Wang, Xiang 1 Wang, Xuefeng 1 Xie, Jinjun 1 Yang, Weihong 1 Zha, Hongyuan 1 Zhang, Shao-Liang 1 Zhang, Wei 1 Zhang, Wei 1 Zhu, Hui June all top 5 Serials 26 Linear Algebra and its Applications 16 SIAM Journal on Matrix Analysis and Applications 8 Mathematics of Computation 8 BIT 6 Numerische Mathematik 4 Mathematica Numerica Sinica 3 Linear and Multilinear Algebra 3 Journal of Computational and Applied Mathematics 3 Journal of Computational Mathematics 3 Science China. Mathematics 2 Applied Mathematics and Computation 2 Journal of Scientific Computing 2 SIAM Journal on Scientific Computing 2 Numerical Linear Algebra with Applications 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 Japan Journal of Industrial and Applied Mathematics 1 SIAM Review 1 SIAM Journal on Optimization 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Chinese Journal of Numerical Mathematics and Applications 1 Optimization Methods & Software 1 Journal of Mathematical Study 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 Fundamentals of Algorithms all top 5 Fields 87 Numerical analysis (65-XX) 75 Linear and multilinear algebra; matrix theory (15-XX) 5 Operator theory (47-XX) 5 Operations research, mathematical programming (90-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 110 Publications have been cited 839 times in 502 Documents Cited by ▼ Year ▼ On the ADI method for Sylvester equations. Zbl 1176.65050Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 55 2009 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010Li, Ren-Cang 40 1998 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 37 2008 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009Li, Ren-Cang 29 1998 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102Bai, Zhaojun; Li, Ren-Cang 23 2013 Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060Kahan, William; Li, Ren-Cang 23 1997 Control parameterization enhancing transform for optimal control of switched systems. Zbl 1139.49030Li, R.; Teo, K. L.; Wong, K. H.; Duan, G. R. 21 2006 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027Li, Chi-Kwong; Li, Ren-Cang 21 2005 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078Bai, Zhaojun; Li, Ren-Cang 20 2012 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 20 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025Xue, Jungong; Xu, Shufang; Li, Ren-Cang 20 2012 A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038Li, Ren-Cang; Ye, Qiang 18 2003 New perturbation bounds for the unitary polar factor. Zbl 0817.15012Li, Ren-Cang 17 1995 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008Li, Ren-Cang 16 2003 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007Li, Ren-Cang 16 1993 On perturbations of matrix pencils with real spectra. Zbl 0795.15012Li, Ren-Cang 15 1994 Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011Li, Ren-Cang 13 1997 A perturbation bound for definite pencils. Zbl 0813.15017Li, Ren-Cang 13 1993 Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022Zhou, Yunkai; Li, Ren-Cang 12 2011 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 12 2006 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028Li, Ren-Cang; Bai, Zhaojun 12 2005 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 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073Li, Ren-Cang; Zhang, Lei-Hong 11 2015 On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027Li, Ren-Cang 11 2008 Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018Li, Ren-Cang 11 1997 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053Xue, Jungong; Xu, Shufang; Li, Ren-Cang 10 2012 Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040Teng, Zhongming; Li, Ren-Cang 9 2013 On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008Bhatia, Rajendra; Li, Ren-Cang 9 1996 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102Zhang, Leihong; Li, Rencang 8 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128Zhang, LeiHong; Li, RenCang 8 2014 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 8 2013 Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh 8 2010 Optimal piecewise state feedback control for impulsive switched systems. Zbl 1145.93352Li, R.; Feng, Z. G.; Teo, K. L.; Duan, G. R. 8 2008 Bounds on perturbations of generalized singular values and of associated subspaces. Zbl 0771.15002Li, Ren-Cang 8 1993 On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006Li, Rencang 8 1992 On the generalized Lanczos trust-region method. Zbl 1380.90210Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 7 2017 Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033Shi, Y. J.; Li, R.; Teo, K. L. 6 2015 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053Bai, Zhaojun; Li, Ren-Cang 6 2014 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038Chang, Xiao-Wen; Li, Ren-Cang 6 2011 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 6 2011 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 6 1997 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049Xue, Jungong; Li, Ren-Cang 5 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 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 5 2016 Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026Shi, Y. J.; Li, R.; Wei, T. T. 5 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 Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang 5 2014 A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080Li, Ren-Cang; Kahan, William 5 2012 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132Li, Ren-Cang 5 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 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016Li, Ren-Cang; Zhang, Wei 5 2009 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025Li, Ren-Cang 5 2008 Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020Li, Ren-Cang 5 2007 Pinchings and norms of scaled triangular matrices. Zbl 1004.15020Bhatia, Rajendra; Kahan, William; Li, Ren-Cang 5 2002 A new relative perturbation theorem for singular subspaces. Zbl 0962.15012Li, Ren-Cang; Stewart, G. W. 5 2000 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017Li, Ren-Cang 5 2000 An Orlicz-Pettis theorem with applications to \(\mathcal A\)-spaces. Zbl 1012.46003Wu, Jun De; Li, R. 5 1999 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018Li, Ren-Cang 5 1999 Spectral variations and Hadamard products: Some problems. Zbl 0933.15032Li, Ren-Cang 5 1998 A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. Zbl 1363.65097Lu, Linzhang; Yuan, Fei; Li, Ren-Cang 4 2015 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033Liang, Xin; Li, Ren-Cang 4 2015 Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 4 2015 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 4 2013 Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang 4 2007 Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang 4 2007 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011Li, Ren-Cang 4 2006 Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010Li, Ren-Cang 4 2005 On the variation of the spectra of matrix pencils. Zbl 0709.15010Li, Rencang 4 1990 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 3 2018 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 3 2016 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021Bai, ZhaoJun; Li, RenCang; Lin, WenWei 3 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 3 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 3 2016 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 3 2015 Monotonicity of unitarily invariant norms. Zbl 1303.15029Wang, Xue-Feng; Li, Ren-Cang 3 2015 An interpolating family of means. Zbl 1331.26053Bhatia, Rajendra; Li, Ren-Cang 3 2012 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033Li, Ren-Cang; Zhang, Wei 3 2009 Hard cases for conjugate gradient method. Zbl 1156.65031Li, Ren-Cang 3 2008 Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036Li, Ren-Cang 3 2004 A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028Truhar, Ninoslav; Li, Ren-Cang 3 2003 Eigenvalues of symmetrizable matrices. Zbl 0898.15015Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 3 1998 QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527Li, Rencang 3 1989 On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504Li, Rencang 3 1989 A converse to the Bauer-Fike type theorem. Zbl 0655.15011Li, Rencang 3 1988 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 2 2016 Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291Wen, M.; Li, R.; Salling, K. B. 2 2016 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053Li, Ren-Cang 2 2015 Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071Li, Ren-Cang; Ye, Qiang 2 2014 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015Liang, Xin; Li, Ren-Cang 2 2014 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 2 2008 The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048Croot, Ernie; Li, Ren-Cang; Zhu, Hui June 2 2004 Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011Li, Rencang 2 1989 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 1 2020 Safe-circumnavigation of one single agent around a group of targets with only bearing information. Zbl 1427.93019Li, R.; Shi, Ying Jing; Wu, X. Q.; Song, Y. D. 1 2019 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 1 2019 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 1 2019 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 1 2018 Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang 1 2017 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 1 2020 Safe-circumnavigation of one single agent around a group of targets with only bearing information. Zbl 1427.93019Li, R.; Shi, Ying Jing; Wu, X. Q.; Song, Y. D. 1 2019 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 1 2019 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 1 2019 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 3 2018 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 1 2018 On the generalized Lanczos trust-region method. Zbl 1380.90210Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 7 2017 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049Xue, Jungong; Li, Ren-Cang 5 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 Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang 1 2017 Optimal parameters for doubling algorithms. Zbl 1413.65138Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang 1 2017 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 5 2016 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 3 2016 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021Bai, ZhaoJun; Li, RenCang; Lin, WenWei 3 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 3 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 3 2016 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 2 2016 Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291Wen, M.; Li, R.; Salling, K. B. 2 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 11 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102Zhang, Leihong; Li, Rencang 8 2015 Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033Shi, Y. J.; Li, R.; Teo, K. L. 6 2015 Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026Shi, Y. J.; Li, R.; Wei, T. T. 5 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 4 2015 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033Liang, Xin; Li, Ren-Cang 4 2015 Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang 4 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 3 2015 Monotonicity of unitarily invariant norms. Zbl 1303.15029Wang, Xue-Feng; Li, Ren-Cang 3 2015 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053Li, Ren-Cang 2 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 8 2014 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053Bai, Zhaojun; Li, Ren-Cang 6 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 2 2014 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015Liang, Xin; Li, Ren-Cang 2 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 23 2013 Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040Teng, Zhongming; Li, Ren-Cang 9 2013 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 8 2013 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 4 2013 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078Bai, Zhaojun; Li, Ren-Cang 20 2012 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 20 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025Xue, Jungong; Xu, Shufang; Li, Ren-Cang 20 2012 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053Xue, Jungong; Xu, Shufang; Li, Ren-Cang 10 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 12 2011 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038Chang, Xiao-Wen; Li, Ren-Cang 6 2011 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 6 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 5 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 55 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 37 2008 On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027Li, Ren-Cang 11 2008 Optimal piecewise state feedback control for impulsive switched systems. Zbl 1145.93352Li, R.; Feng, Z. G.; Teo, K. L.; Duan, G. R. 8 2008 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025Li, Ren-Cang 5 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 Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang 4 2007 Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang 4 2007 Tracking control of linear switched systems. Zbl 1147.49033Li, R.; Feng, Z. G.; Teo, K. L.; Duan, G. R. 1 2007 Control parameterization enhancing transform for optimal control of switched systems. Zbl 1139.49030Li, R.; Teo, K. L.; Wong, K. H.; Duan, G. R. 21 2006 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 12 2006 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011Li, Ren-Cang 4 2006 Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008Li, Ren-Cang 1 2006 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027Li, Chi-Kwong; Li, Ren-Cang 21 2005 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028Li, Ren-Cang; Bai, Zhaojun 12 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 3 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 18 2003 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008Li, Ren-Cang 16 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 5 2002 A new relative perturbation theorem for singular subspaces. Zbl 0962.15012Li, Ren-Cang; Stewart, G. W. 5 2000 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017Li, Ren-Cang 5 2000 An Orlicz-Pettis theorem with applications to \(\mathcal A\)-spaces. Zbl 1012.46003Wu, Jun De; Li, R. 5 1999 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018Li, Ren-Cang 5 1999 Hypocontinuity and uniform boundedness for bilinear maps. Zbl 0938.47046Wu, Jun De; Li, R. 1 1999 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010Li, Ren-Cang 40 1998 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009Li, Ren-Cang 29 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 23 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 11 1997 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 6 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 17 1995 On perturbations of matrix pencils with real spectra. Zbl 0795.15012Li, Ren-Cang 15 1994 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007Li, Ren-Cang 16 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 675 Authors 58 Li, Rencang 19 Benner, Peter 15 Li, Wen 15 Zhang, Lei-Hong 14 Lin, Wen-Wei 14 Truhar, Ninoslav 12 Dopico, Froilán M. 9 Bai, Zhaojun 9 Nakatsukasa, Yuji 9 Reichel, Lothar 8 Li, Hanyu 8 Ma, Changfeng 8 Shen, Chungen 8 Ye, Qiang 7 Kressner, Daniel 7 Kürschner, Patrick 7 Wei, Yimin 6 Chen, Xiaoshan 6 Feng, Enmin 6 Liu, Chongyang 6 Saak, Jens 6 Su, Yangfeng 6 Tisseur, Françoise 6 Yang, Weihong 5 Bhatia, Rajendra 5 Blanes, Sergio 5 Gong, Zhaohua 5 Lawrence, Piers W. 5 Meng, Lingsheng 5 Simoncini, Valeria 5 Slapničar, Ivan 5 Teng, Zhongming 5 Teo, Kok Lay 5 Townsend, Alex 5 Xu, Wei-Wei 5 Yang, Chao 5 Yang, Hu 5 Zheng, Bing 5 Zhou, Yunkai 4 Dai, Hua 4 de Terán, Fernando 4 Guo, Chun-Hua 4 Huang, Tsungming 4 Ipsen, Ilse C. F. 4 Kittaneh, Fuad 4 Li, Tiexiang 4 Lu, Linzhang 4 Saad, Yousef 4 Shi, Yingjing 4 Tomljanović, Zoran 4 Wang, Weiguo 4 Xue, Jungong 3 Casas, Fernando 3 Chen, Xiaoping 3 Chu, Delin 3 Doostaki, Reza 3 Furtado, Susana 3 Grubišić, Luka 3 Hochstenbach, Michiel E. 3 Huang, Na 3 Huang, Rong 3 Huang, Weiqiang 3 Imakura, Akira 3 Jbilou, Khalide 3 Khoromskij, Boris N. 3 Kuo, Yueh-Cheng 3 Li, Chi-Kwong 3 Li, Jicheng 3 Li, Yung-Ta 3 Liu, Landong 3 Loxton, Ryan Christopher 3 Molera, Juan M. 3 Pandur, Marija Miloloža 3 Parlett, Beresford Neill 3 Plešinger, Martin 3 Rehman, Abdur 3 Safique Ahmad, Sk. 3 Shao, Meiyue 3 Thalhammer, Mechthild 3 Veselić, Krešimir 3 Wang, Qingwen 3 Wang, Xiang 3 Wen, Zaiwen 3 Wu, Guoxing 3 Xi, Yuanzhe 3 Xu, Qingxiang 3 Xu, Shufang 3 Zhi, Weifeng 3 Zhu, Lei 2 Abdel-Aziz, Mohammedi R. 2 Adhikari, Bibhas 2 Akram, Muhammad 2 Alam, Rafikul 2 Ali, Ilyas 2 Bao, Liang 2 Beckermann, Bernhard 2 Bouhamidi, Abderrahman 2 Breiten, Tobias 2 Bueno, María Isabel 2 Bueno, Maribel I. ...and 575 more Authors all top 5 Cited in 123 Serials 83 Linear Algebra and its Applications 25 SIAM Journal on Matrix Analysis and Applications 23 Journal of Computational and Applied Mathematics 22 Numerische Mathematik 18 BIT 16 Applied Mathematics and Computation 16 SIAM Journal on Scientific Computing 15 Linear and Multilinear Algebra 14 Mathematics of Computation 13 Numerical Algorithms 13 Numerical Linear Algebra with Applications 10 Applied Numerical Mathematics 9 Computers & Mathematics with Applications 9 Journal of Scientific Computing 8 Journal of Computational Physics 7 Automatica 7 International Journal of Computer Mathematics 6 Calcolo 6 SIAM Journal on Optimization 5 SIAM Review 5 Computational and Applied Mathematics 5 ETNA. 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Principles and Applications of Systems and Integration 1 International Journal of Control 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Engineering Mathematics 1 Rocky Mountain Journal of Mathematics 1 Arkiv för Matematik 1 Chaos, Solitons and Fractals 1 ACM Transactions on Mathematical Software 1 Integral Equations and Operator Theory 1 Journal of Computer and System Sciences 1 Mathematische Zeitschrift 1 Theoretical Computer Science 1 Zeitschrift für Analysis und ihre Anwendungen 1 Optimization 1 Queueing Systems 1 Annals of Operations Research 1 Journal of Global Optimization 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 Computational Optimization and Applications 1 Applied and Computational Harmonic Analysis 1 Algebra Colloquium 1 Advances in Applied Clifford Algebras 1 Journal of Computational Neuroscience 1 Bernoulli 1 ELA. The Electronic Journal of Linear Algebra 1 Mathematical Problems in Engineering 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 International Journal of Applied Mathematics and Computer Science 1 RAIRO. Theoretical Informatics and Applications 1 Optimization and Engineering 1 Archives of Computational Methods in Engineering 1 Foundations of Computational Mathematics 1 Computational Methods in Applied Mathematics 1 Journal of Applied Mathematics 1 Natural Computing 1 Journal of Applied Mathematics and Computing ...and 23 more Serials all top 5 Cited in 36 Fields 350 Numerical analysis (65-XX) 271 Linear and multilinear algebra; matrix theory (15-XX) 52 Systems theory; control (93-XX) 36 Operations research, mathematical programming (90-XX) 28 Operator theory (47-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 26 Ordinary differential equations (34-XX) 16 Partial differential equations (35-XX) 16 Computer science (68-XX) 12 Biology and other natural sciences (92-XX) 11 Dynamical systems and ergodic theory (37-XX) 9 Probability theory and stochastic processes (60-XX) 7 Mechanics of particles and systems (70-XX) 7 Fluid mechanics (76-XX) 6 Real functions (26-XX) 6 Functions of a complex variable (30-XX) 5 Approximations and expansions (41-XX) 4 Sequences, series, summability (40-XX) 4 Functional analysis (46-XX) 3 Combinatorics (05-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 Statistics (62-XX) 3 Mechanics of deformable solids (74-XX) 3 Quantum theory (81-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Number theory (11-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 General topology (54-XX) 2 Optics, electromagnetic theory (78-XX) 1 Nonassociative rings and algebras (17-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year