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 Documents Indexed: 128 Publications since 1988, including 1 Book Co-Authors: 60 Co-Authors with 80 Joint Publications 2,543 Co-Co-Authors all top 5 Co-Authors 36 single-authored 12 Bai, Zhaojun 12 Zhang, Lei-Hong 8 Truhar, Ninoslav 7 Lu, Linzhang 6 Xue, Jungong 5 Bhatia, Rajendra 5 Wang, Weiguo 5 Xu, Shufang 5 Ye, Qiang 4 Lin, Wen-Wei 4 Teng, Zhongming 4 Teo, Kok Lay 3 Duan, Guangren 3 Huang, Tsungming 3 Kahan, William Morton 3 Liang, Xin 3 Liu, Changli 3 Nakatsukasa, Yuji 3 Shen, Chungen 2 Cai, Yunfeng 2 Feng, Zhiguo 2 Garrett, C. Kristopher 2 Kittaneh, Fuad 2 Li, Chi-Kwong 2 Lin, Wenwei 2 Shi, Yingjing 2 Tomljanović, Zoran 2 Wang, Weichao 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 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 Lu, Ding 1 Ma, Changfeng 1 Ma, Xijun 1 Overton, Michael L. 1 Salling, K. B. 1 Shao, Rongxia 1 Song, Yongduan 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 26 Linear Algebra and its Applications 17 SIAM Journal on Matrix Analysis and Applications 8 Mathematics of Computation 8 BIT 6 Numerische Mathematik 5 Journal of Computational and Applied Mathematics 4 Mathematica Numerica Sinica 3 Linear and Multilinear Algebra 3 Journal of Computational Mathematics 3 The ANZIAM Journal 3 Science China. Mathematics 2 Applied Mathematics and Computation 2 Mathematical and Computer Modelling 2 Journal of Scientific Computing 2 SIAM Journal on Scientific Computing 2 Numerical Linear Algebra with Applications 2 Advances in Computational Mathematics 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 International Journal of Control 1 Journal of the Franklin Institute 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 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 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 91 Numerical analysis (65-XX) 76 Linear and multilinear algebra; matrix theory (15-XX) 12 Systems theory; control (93-XX) 9 Operations research, mathematical programming (90-XX) 6 Operator theory (47-XX) 4 Ordinary differential equations (34-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 2 Statistics (62-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 Mechanics of deformable solids (74-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 111 Publications have been cited 973 times in 546 Documents Cited by ▼ Year ▼ On the ADI method for Sylvester equations. Zbl 1176.65050Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 65 2009 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010Li, Ren-Cang 47 1998 Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise 41 2008 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009Li, Ren-Cang 36 1998 Control parameterization enhancing transform for optimal control of switched systems. Zbl 1139.49030Li, R.; Teo, K. L.; Wong, K. H.; Duan, G. R. 28 2006 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102Bai, Zhaojun; Li, Ren-Cang 27 2013 Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060Kahan, William; Li, Ren-Cang 25 1997 Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 25 2012 A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027Li, Chi-Kwong; Li, Ren-Cang 24 2005 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078Bai, Zhaojun; Li, Ren-Cang 24 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025Xue, Jungong; Xu, Shufang; Li, Ren-Cang 22 2012 New perturbation bounds for the unitary polar factor. Zbl 0817.15012Li, Ren-Cang 20 1995 A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038Li, Ren-Cang; Ye, Qiang 19 2003 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008Li, Ren-Cang 17 2003 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028Li, Ren-Cang; Bai, Zhaojun 17 2005 A perturbation bound for the generalized polar decomposition. Zbl 0785.15007Li, Ren-Cang 16 1993 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073Li, Ren-Cang; Zhang, Lei-Hong 15 2015 On perturbations of matrix pencils with real spectra. Zbl 0795.15012Li, Ren-Cang 14 1994 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 14 2018 A perturbation bound for definite pencils. Zbl 0813.15017Li, Ren-Cang 13 1993 Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128Zhang, LeiHong; Li, RenCang 13 2014 Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011Li, Ren-Cang 13 1997 Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022Zhou, Yunkai; Li, Ren-Cang 13 2011 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102Zhang, Leihong; Li, Rencang 12 2015 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 Krylov type subspace methods for matrix polynomials. Zbl 1104.65032Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang 12 2006 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053Xue, Jungong; Xu, Shufang; Li, Ren-Cang 11 2012 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 On the generalized Lanczos trust-region method. Zbl 1380.90210Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 10 2017 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 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 9 2013 On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006Li, Rencang 8 1992 Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033Shi, Y. J.; Li, R.; Teo, K. L. 8 2015 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 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038Chang, Xiao-Wen; Li, Ren-Cang 8 2011 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053Bai, Zhaojun; Li, Ren-Cang 8 2014 Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang 7 2011 QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527Li, Rencang 7 1989 A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018Li, Ren-Cang 7 1999 Pinchings and norms of scaled triangular matrices. Zbl 1004.15020Bhatia, Rajendra; Kahan, William; Li, Ren-Cang 7 2002 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053Li, Ren-Cang 6 2015 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049Xue, Jungong; Li, Ren-Cang 6 2017 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 Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 6 1997 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 symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei 5 2017 A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080Li, Ren-Cang; Kahan, William 5 2012 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 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132Li, Ren-Cang 5 2010 Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020Li, Ren-Cang 5 2007 Spectral variations and Hadamard products: Some problems. Zbl 0933.15032Li, Ren-Cang 5 1998 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016Li, Ren-Cang; Zhang, Wei 5 2009 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 5 2020 Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025Li, Ren-Cang 5 2008 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021Bai, ZhaoJun; Li, RenCang; Lin, WenWei 5 2016 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 5 2016 Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang 5 2014 Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026Shi, Y. J.; Li, R.; Wei, T. T. 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 4 2015 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033Liang, Xin; Li, Ren-Cang 4 2015 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 On the variation of the spectra of matrix pencils. Zbl 0709.15010Li, Rencang 4 1990 Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011Li, Ren-Cang 4 2006 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 Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017Li, Ren-Cang 4 2000 Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036Li, Ren-Cang 4 2004 Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010Li, Ren-Cang 4 2005 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 Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang 4 2013 An interpolating family of means. Zbl 1331.26053Bhatia, Rajendra; Li, Ren-Cang 3 2012 Algorithms for inverse eigenvalue problems. Zbl 0751.65027Li, Rencang 3 1992 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 3 2016 Monotonicity of unitarily invariant norms. Zbl 1303.15029Wang, Xue-Feng; Li, Ren-Cang 3 2015 Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071Li, Ren-Cang; Ye, Qiang 3 2014 Eigenvalues of symmetrizable matrices. Zbl 0898.15015Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang 3 1998 The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033Li, Ren-Cang; Zhang, Wei 3 2009 A converse to the Bauer-Fike type theorem. Zbl 0655.15011Li, Rencang 3 1988 A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028Truhar, Ninoslav; Li, Ren-Cang 3 2003 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 3 2019 Hard cases for conjugate gradient method. Zbl 1156.65031Li, Ren-Cang 3 2008 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 3 2016 Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015Liang, Xin; Li, Ren-Cang 2 2014 On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504Li, Rencang 2 1989 The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048Croot, Ernie; Li, Ren-Cang; Zhu, Hui June 2 2004 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011Li, Rencang 2 1989 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 2 2018 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. 2 2019 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 2 2020 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 2 2008 Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291Wen, M.; Li, R.; Salling, K. B. 2 2016 Optimal parameters for doubling algorithms. Zbl 1413.65138Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang 2 2017 First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. 5 2020 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 2 2020 Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations. Zbl 1445.65012Liu, Changli; Xue, Jungong; Li, Ren-Cang 1 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 3 2019 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. 2 2019 Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022Chen, Cairong; Li, Ren-Cang; Ma, Changfeng 2 2019 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 14 2018 Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei 2 2018 On the generalized Lanczos trust-region method. Zbl 1380.90210Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang 10 2017 Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049Xue, Jungong; Li, Ren-Cang 6 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. 1 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 5 2016 A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang 5 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 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 nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 3 2016 Locally optimal and heavy ball GMRES methods. Zbl 1354.65063Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang 3 2016 Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia 2 2016 Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291Wen, M.; Li, R.; Salling, K. B. 2 2016 Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073Li, Ren-Cang; Zhang, Lei-Hong 15 2015 Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102Zhang, Leihong; Li, Rencang 12 2015 Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033Shi, Y. J.; Li, R.; Teo, K. L. 8 2015 Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053Li, 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 Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026Shi, Y. J.; Li, R.; Wei, T. T. 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 4 2015 The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033Liang, Xin; Li, Ren-Cang 4 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 13 2014 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053Bai, Zhaojun; Li, Ren-Cang 8 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 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 27 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 9 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 25 2012 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078Bai, Zhaojun; Li, Ren-Cang 24 2012 Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025Xue, Jungong; Xu, Shufang; Li, Ren-Cang 22 2012 Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053Xue, Jungong; Xu, Shufang; Li, Ren-Cang 11 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 13 2011 Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038Chang, Xiao-Wen; Li, Ren-Cang 8 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 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 Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132Li, Ren-Cang 5 2010 On the ADI method for Sylvester equations. Zbl 1176.65050Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav 65 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 41 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 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 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. 28 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 24 2005 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028Li, Ren-Cang; Bai, Zhaojun 17 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 4 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 19 2003 On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008Li, Ren-Cang 17 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 7 1999 Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010Li, Ren-Cang 47 1998 Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009Li, Ren-Cang 36 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 25 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 20 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 16 1993 ...and 11 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 683 Authors 61 Li, Rencang 20 Benner, Peter 19 Zhang, Lei-Hong 15 Truhar, Ninoslav 12 Dopico, Froilán M. 11 Li, Hanyu 11 Li, Wen 11 Shen, Chungen 10 Bai, Zhaojun 9 Lin, Wen-Wei 9 Nakatsukasa, Yuji 9 Reichel, Lothar 8 Kressner, Daniel 8 Kürschner, Patrick 8 Ma, Changfeng 8 Ye, Qiang 7 Chen, Xiaoshan 7 Wang, Xiang 7 Wei, Yimin 7 Yang, Weihong 6 Chen, Xiaoping 6 Dai, Hua 6 Kittaneh, Fuad 6 Saak, Jens 6 Su, Yangfeng 6 Tisseur, Françoise 6 Townsend, Alex 6 Zheng, Bing 5 Bhatia, Rajendra 5 Blanes, Sergio 5 Chen, Hongjia 5 Lawrence, Piers W. 5 Meng, Lingsheng 5 Simoncini, Valeria 5 Slapničar, Ivan 5 Teng, Zhongming 5 Wang, Weiguo 5 Xu, Wei-Wei 5 Xue, Jungong 5 Yang, Hu 5 Zhou, Yunkai 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 Saad, Yousef 4 Tomljanović, Zoran 4 Xi, Yuanzhe 4 Xu, Qingxiang 3 Beckermann, Bernhard 3 Casas, Fernando 3 Chen, Cairong 3 Chu, Delin 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 Jbilou, Khalide 3 Jia, Zhongxiao 3 Khoromskiĭ, Boris Nikolaevich 3 Kuo, Yueh-Cheng 3 Li, Chi-Kwong 3 Li, Yung-Ta 3 Liang, Xin 3 Liu, Changli 3 Massey, Pedro G. 3 Miodragović, Suzana 3 Molera, Juan M. 3 Pandur, Marija Miloloža 3 Parlett, Beresford Neill 3 Pérez, Javier J. 3 Plešinger, Martin 3 Rehman, Abdur 3 Safique Ahmad, Sk. 3 Samar, Mahvish 3 Shao, Meiyue 3 Stojanoff, Demetrio 3 Stykel, Tatjana 3 Thalhammer, Mechthild 3 Veselić, Krešimir 3 Wang, Qingwen 3 Wen, Zaiwen 3 Wu, Guoxing 3 Xiao, Chuanfu 3 Xu, Shufang 3 Yang, Chao 3 Yang, Xi ...and 583 more Authors all top 5 Cited in 137 Serials 87 Linear Algebra and its Applications 33 SIAM Journal on Matrix Analysis and Applications 27 Journal of Computational and Applied Mathematics 23 Numerische Mathematik 21 SIAM Journal on Scientific Computing 20 BIT 18 Linear and Multilinear Algebra 18 Applied Mathematics and Computation 15 Numerical Algorithms 14 Mathematics of Computation 13 Numerical Linear Algebra with Applications 12 Applied Numerical Mathematics 11 Computers & Mathematics with Applications 11 Journal of Scientific Computing 10 Journal of Computational Physics 9 International Journal of Computer Mathematics 8 SIAM Journal on Optimization 7 Calcolo 7 East Asian Journal on Applied Mathematics 6 ETNA. 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The Electronic Journal of Linear Algebra 2 Taiwanese Journal of Mathematics 2 Mathematical Inequalities & Applications 2 Acta Mathematica Sinica. English Series 2 Stochastic Models 2 Journal of Machine Learning Research (JMLR) 2 Journal of Applied Mathematics and Computing 2 Communications on Applied Mathematics and Computation 1 Indian Journal of Pure & Applied Mathematics 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 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 Journal of Optimization Theory and Applications 1 Journal of Statistical Planning and Inference 1 Mathematics and Computers in Simulation 1 Mathematische Zeitschrift 1 Theoretical Computer Science 1 Optimization 1 Mathematical and Computer Modelling 1 Queueing Systems 1 Science in China. Series A 1 Annals of Operations Research 1 Aequationes Mathematicae 1 Applied Mathematical Modelling 1 Glasnik Matematički. Serija III 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Computational Statistics and Data Analysis 1 Applied and Computational Harmonic Analysis 1 Algebra Colloquium 1 Advances in Applied Clifford Algebras 1 Filomat 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 International Journal of Applied Mathematics and Computer Science 1 RAIRO. Theoretical Informatics and Applications 1 Econometric Theory 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 Advanced Nonlinear Studies 1 Natural Computing ...and 37 more Serials all top 5 Cited in 36 Fields 400 Numerical analysis (65-XX) 307 Linear and multilinear algebra; matrix theory (15-XX) 40 Operator theory (47-XX) 40 Operations research, mathematical programming (90-XX) 31 Systems theory; control (93-XX) 21 Ordinary differential equations (34-XX) 20 Partial differential equations (35-XX) 16 Computer science (68-XX) 12 Dynamical systems and ergodic theory (37-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 9 Probability theory and stochastic processes (60-XX) 8 Functions of a complex variable (30-XX) 8 Mechanics of particles and systems (70-XX) 8 Quantum theory (81-XX) 7 Fluid mechanics (76-XX) 6 Real functions (26-XX) 6 Approximations and expansions (41-XX) 6 Biology and other natural sciences (92-XX) 4 Combinatorics (05-XX) 4 Special functions (33-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Statistics (62-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Difference and functional equations (39-XX) 3 Mechanics of deformable solids (74-XX) 3 Information and communication theory, circuits (94-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) 1 Sequences, series, summability (40-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) Citations by Year