## Li, Rencang

Compute Distance To:
 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)

### 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 1176.65050
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav
2009
Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010
Li, Ren-Cang
1998
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
2008
Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009
Li, Ren-Cang
1998
Control parameterization enhancing transform for optimal control of switched systems. Zbl 1139.49030
Li, R.; Teo, K. L.; Wong, K. H.; Duan, G. R.
2006
Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102
Bai, Zhaojun; Li, Ren-Cang
2013
Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060
Kahan, William; Li, Ren-Cang
1997
Alternating-directional doubling algorithm for $$M$$-matrix algebraic Riccati equations. Zbl 1258.65045
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
2012
A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027
Li, Chi-Kwong; Li, Ren-Cang
2005
Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078
Bai, Zhaojun; Li, Ren-Cang
2012
Accurate solutions of $$M$$-matrix algebraic Riccati equations. Zbl 1260.15025
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
2012
New perturbation bounds for the unitary polar factor. Zbl 0817.15012
Li, Ren-Cang
1995
A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038
Li, Ren-Cang; Ye, Qiang
2003
On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008
Li, Ren-Cang
2003
Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028
Li, Ren-Cang; Bai, Zhaojun
2005
A perturbation bound for the generalized polar decomposition. Zbl 0785.15007
Li, Ren-Cang
1993
Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073
Li, Ren-Cang; Zhang, Lei-Hong
2015
On perturbations of matrix pencils with real spectra. Zbl 0795.15012
Li, Ren-Cang
1994
On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036
Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang
2018
A perturbation bound for definite pencils. Zbl 0813.15017
Li, Ren-Cang
1993
Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128
Zhang, LeiHong; Li, RenCang
2014
Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011
Li, Ren-Cang
1997
Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022
Zhou, Yunkai; Li, Ren-Cang
2011
Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102
Zhang, Leihong; Li, Rencang
2015
A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017
Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang
1996
Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. Zbl 0770.15009
Li, Rencang
1993
Krylov type subspace methods for matrix polynomials. Zbl 1104.65032
Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang
2006
Accurate solutions of $$M$$-matrix Sylvester equations. Zbl 1245.65053
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
2012
On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027
Li, Ren-Cang
2008
Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018
Li, Ren-Cang
1997
On the generalized Lanczos trust-region method. Zbl 1380.90210
Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang
2017
Bounds on perturbations of generalized singular values and of associated subspaces. Zbl 0771.15002
Li, Ren-Cang
1993
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
1996
Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040
Teng, Zhongming; Li, Ren-Cang
2013
Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010
Liang, Xin; Li, Ren-Cang; Bai, Zhaojun
2013
On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006
Li, Rencang
1992
Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033
Shi, Y. J.; Li, R.; Teo, K. L.
2015
Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063
Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh
2010
Optimal piecewise state feedback control for impulsive switched systems. Zbl 1145.93352
Li, R.; Feng, Z. G.; Teo, K. L.; Duan, G. R.
2008
Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038
Chang, Xiao-Wen; Li, Ren-Cang
2011
Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053
Bai, Zhaojun; Li, Ren-Cang
2014
Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang
2011
QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527
Li, Rencang
1989
A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018
Li, Ren-Cang
1999
Pinchings and norms of scaled triangular matrices. Zbl 1004.15020
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang
2002
Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053
Li, Ren-Cang
2015
Highly accurate doubling algorithms for $$M$$-matrix algebraic Riccati equations. Zbl 1362.65049
Xue, Jungong; Li, Ren-Cang
2017
Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
2015
A new relative perturbation theorem for singular subspaces. Zbl 0962.15012
Li, Ren-Cang; Stewart, G. W.
2000
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1997
Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem. Zbl 1350.65081
Zhang, Lei-Hong; Lin, Wen-Wei; Li, Ren-Cang
2015
A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. Zbl 1363.65097
Lu, Linzhang; Yuan, Fei; Li, Ren-Cang
2015
A symmetric structure-preserving {$$\Gamma$$}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057
Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei
2017
A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080
Li, Ren-Cang; Kahan, William
2012
Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. Zbl 1193.65045
Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang
2010
Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132
Li, Ren-Cang
2010
Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020
Li, Ren-Cang
2007
Spectral variations and Hadamard products: Some problems. Zbl 0933.15032
Li, Ren-Cang
1998
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016
Li, Ren-Cang; Zhang, Wei
2009
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
2020
Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025
Li, Ren-Cang
2008
Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021
Bai, ZhaoJun; Li, RenCang; Lin, WenWei
2016
A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046
Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang
2016
Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126
Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang
2014
Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026
Shi, Y. J.; Li, R.; Wei, T. T.
2015
A Krylov subspace method for large-scale second-order cone linear complementarity problem. Zbl 1326.90090
Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang
2015
The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033
Liang, Xin; Li, Ren-Cang
2015
A new two-phase structure-preserving doubling algorithm for critically singular $$M$$-matrix algebraic Riccati equations. Zbl 1374.65068
Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei
2016
On the variation of the spectra of matrix pencils. Zbl 0709.15010
Li, Rencang
1990
Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011
Li, Ren-Cang
2006
Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang
2007
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
2007
Relative perturbation theory. IV: $$\sin 2\theta$$ theorems. Zbl 0963.15017
Li, Ren-Cang
2000
Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036
Li, Ren-Cang
2004
Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010
Li, Ren-Cang
2005
A fast algorithm for fast train palindromic quadratic eigenvalue problems. Zbl 1352.65121
Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei
2016
Deflating irreducible singular $$M$$-matrix Algebraic Riccati Equations. Zbl 1271.15005
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
2013
An interpolating family of means. Zbl 1331.26053
Bhatia, Rajendra; Li, Ren-Cang
2012
Algorithms for inverse eigenvalue problems. Zbl 0751.65027
Li, Rencang
1992
A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057
Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang
2016
Monotonicity of unitarily invariant norms. Zbl 1303.15029
Wang, Xue-Feng; Li, Ren-Cang
2015
Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071
Li, Ren-Cang; Ye, Qiang
2014
Eigenvalues of symmetrizable matrices. Zbl 0898.15015
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1998
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033
Li, Ren-Cang; Zhang, Wei
2009
A converse to the Bauer-Fike type theorem. Zbl 0655.15011
Li, Rencang
1988
A $$\sin 2\varTheta$$ theorem for graded indefinite Hermitian matrices. Zbl 1025.15028
Truhar, Ninoslav; Li, Ren-Cang
2003
An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem. Zbl 1418.90265
Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang
2019
Hard cases for conjugate gradient method. Zbl 1156.65031
Li, Ren-Cang
2008
Locally optimal and heavy ball GMRES methods. Zbl 1354.65063
Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang
2016
Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015
Liang, Xin; Li, Ren-Cang
2014
On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504
Li, Rencang
1989
The $$abc$$ conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048
Croot, Ernie; Li, Ren-Cang; Zhu, Hui June
2004
Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia
2016
Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011
Li, Rencang
1989
Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006
Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei
2018
Safe-circumnavigation of one single agent around a group of targets with only bearing information. Zbl 1427.93019
Li, R.; Shi, Ying Jing; Wu, X. Q.; Song, Y. D.
2019
Orthogonal canonical correlation analysis and applications. Zbl 1455.65059
Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang
2020
A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010
Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng
2008
Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291
Wen, M.; Li, R.; Salling, K. B.
2016
Optimal parameters for doubling algorithms. Zbl 1413.65138
Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang
2017
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
2020
Orthogonal canonical correlation analysis and applications. Zbl 1455.65059
Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang
2020
Accurate numerical solution for shifted $$M$$-matrix algebraic Riccati equations. Zbl 1445.65012
Liu, Changli; Xue, Jungong; Li, Ren-Cang
2020
An efficient numerical method for the symmetric positive definite second-order cone linear complementarity problem. Zbl 1418.90265
Wang, Xiang; Li, Xing; Zhang, Lei-Hong; Li, Ren-Cang
2019
Safe-circumnavigation of one single agent around a group of targets with only bearing information. Zbl 1427.93019
Li, R.; Shi, Ying Jing; Wu, X. Q.; Song, Y. D.
2019
Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022
Chen, Cairong; Li, Ren-Cang; Ma, Changfeng
2019
On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036
Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang
2018
Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006
Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei
2018
On the generalized Lanczos trust-region method. Zbl 1380.90210
Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang
2017
Highly accurate doubling algorithms for $$M$$-matrix algebraic Riccati equations. Zbl 1362.65049
Xue, Jungong; Li, Ren-Cang
2017
A symmetric structure-preserving {$$\Gamma$$}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057
Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei
2017
Optimal parameters for doubling algorithms. Zbl 1413.65138
Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang
2017
Rotary enclosing control of second-order multi-agent systems for a group of targets. Zbl 1358.93017
Shi, Y. J.; Li, R.; Teo, K. L.
2017
Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016
Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang
2017
Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021
Bai, ZhaoJun; Li, RenCang; Lin, WenWei
2016
A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046
Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang
2016
A new two-phase structure-preserving doubling algorithm for critically singular $$M$$-matrix algebraic Riccati equations. Zbl 1374.65068
Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei
2016
A fast algorithm for fast train palindromic quadratic eigenvalue problems. Zbl 1352.65121
Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei
2016
A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057
Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang
2016
Locally optimal and heavy ball GMRES methods. Zbl 1354.65063
Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang
2016
Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia
2016
Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291
Wen, M.; Li, R.; Salling, K. B.
2016
Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073
Li, Ren-Cang; Zhang, Lei-Hong
2015
Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102
Zhang, Leihong; Li, Rencang
2015
Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033
Shi, Y. J.; Li, R.; Teo, K. L.
2015
Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053
Li, Ren-Cang
2015
Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
2015
Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem. Zbl 1350.65081
Zhang, Lei-Hong; Lin, Wen-Wei; Li, Ren-Cang
2015
A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. Zbl 1363.65097
Lu, Linzhang; Yuan, Fei; Li, Ren-Cang
2015
Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026
Shi, Y. J.; Li, R.; Wei, T. T.
2015
A Krylov subspace method for large-scale second-order cone linear complementarity problem. Zbl 1326.90090
Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang
2015
The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033
Liang, Xin; Li, Ren-Cang
2015
Monotonicity of unitarily invariant norms. Zbl 1303.15029
Wang, Xue-Feng; Li, Ren-Cang
2015
Perturbation of partitioned linear response eigenvalue problems. Zbl 1330.65060
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
2015
Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128
Zhang, LeiHong; Li, RenCang
2014
Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053
Bai, Zhaojun; Li, Ren-Cang
2014
Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126
Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang
2014
Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071
Li, Ren-Cang; Ye, Qiang
2014
Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015
Liang, Xin; Li, Ren-Cang
2014
GIP integrators for matrix Riccati differential equations. Zbl 1337.65074
Kristopher Garrett, C.; Li, Ren-Cang
2014
Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102
Bai, Zhaojun; Li, Ren-Cang
2013
Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040
Teng, Zhongming; Li, Ren-Cang
2013
Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010
Liang, Xin; Li, Ren-Cang; Bai, Zhaojun
2013
Deflating irreducible singular $$M$$-matrix Algebraic Riccati Equations. Zbl 1271.15005
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
2013
Alternating-directional doubling algorithm for $$M$$-matrix algebraic Riccati equations. Zbl 1258.65045
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
2012
Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078
Bai, Zhaojun; Li, Ren-Cang
2012
Accurate solutions of $$M$$-matrix algebraic Riccati equations. Zbl 1260.15025
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
2012
Accurate solutions of $$M$$-matrix Sylvester equations. Zbl 1245.65053
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
2012
A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080
Li, Ren-Cang; Kahan, William
2012
An interpolating family of means. Zbl 1331.26053
Bhatia, Rajendra; Li, Ren-Cang
2012
Perturbation of multiple eigenvalues of Hermitian matrices. Zbl 1242.15016
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Wang, Wei-Guo
2012
Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022
Zhou, Yunkai; Li, Ren-Cang
2011
Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038
Chang, Xiao-Wen; Li, Ren-Cang
2011
Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang
2011
Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035
Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang
2011
Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063
Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh
2010
Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. Zbl 1193.65045
Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang
2010
Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132
Li, Ren-Cang
2010
On the ADI method for Sylvester equations. Zbl 1176.65050
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav
2009
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016
Li, Ren-Cang; Zhang, Wei
2009
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033
Li, Ren-Cang; Zhang, Wei
2009
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
2008
On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027
Li, Ren-Cang
2008
Optimal piecewise state feedback control for impulsive switched systems. Zbl 1145.93352
Li, R.; Feng, Z. G.; Teo, K. L.; Duan, G. R.
2008
Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025
Li, Ren-Cang
2008
Hard cases for conjugate gradient method. Zbl 1156.65031
Li, Ren-Cang
2008
A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010
Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng
2008
Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020
Li, Ren-Cang
2007
Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang
2007
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
2007
Tracking control of linear switched systems. Zbl 1147.49033
Li, R.; Feng, Z. G.; Teo, K. L.; Duan, G. R.
2007
Control parameterization enhancing transform for optimal control of switched systems. Zbl 1139.49030
Li, R.; Teo, K. L.; Wong, K. H.; Duan, G. R.
2006
Krylov type subspace methods for matrix polynomials. Zbl 1104.65032
Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang
2006
Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011
Li, Ren-Cang
2006
Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008
Li, Ren-Cang
2006
A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027
Li, Chi-Kwong; Li, Ren-Cang
2005
Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028
Li, Ren-Cang; Bai, Zhaojun
2005
Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010
Li, Ren-Cang
2005
Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036
Li, Ren-Cang
2004
The $$abc$$ conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048
Croot, Ernie; Li, Ren-Cang; Zhu, Hui June
2004
A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038
Li, Ren-Cang; Ye, Qiang
2003
On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008
Li, Ren-Cang
2003
A $$\sin 2\varTheta$$ theorem for graded indefinite Hermitian matrices. Zbl 1025.15028
Truhar, Ninoslav; Li, Ren-Cang
2003
Pinchings and norms of scaled triangular matrices. Zbl 1004.15020
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang
2002
A new relative perturbation theorem for singular subspaces. Zbl 0962.15012
Li, Ren-Cang; Stewart, G. W.
2000
Relative perturbation theory. IV: $$\sin 2\theta$$ theorems. Zbl 0963.15017
Li, Ren-Cang
2000
A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018
Li, Ren-Cang
1999
Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010
Li, Ren-Cang
1998
Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009
Li, Ren-Cang
1998
Spectral variations and Hadamard products: Some problems. Zbl 0933.15032
Li, Ren-Cang
1998
Eigenvalues of symmetrizable matrices. Zbl 0898.15015
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1998
Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060
Kahan, William; Li, Ren-Cang
1997
Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011
Li, Ren-Cang
1997
Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018
Li, Ren-Cang
1997
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1997
A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017
Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang
1996
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
1996
New perturbation bounds for the unitary polar factor. Zbl 0817.15012
Li, Ren-Cang
1995
On perturbations of matrix pencils with real spectra. Zbl 0795.15012
Li, Ren-Cang
1994
A perturbation bound for the generalized polar decomposition. Zbl 0785.15007
Li, Ren-Cang
1993
...and 11 more Documents
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. Electronic Transactions on Numerical Analysis 5 SIAM Review 5 Computational and Applied Mathematics 5 Science China. Mathematics 4 Applied Mathematics Letters 4 Advances in Computational Mathematics 4 Numerical Algebra, Control and Optimization 3 Journal of Mathematical Analysis and Applications 3 Automatica 3 SIAM Journal on Numerical Analysis 3 Japan Journal of Industrial and Applied Mathematics 3 Optimization Methods & Software 3 Frontiers of Mathematics in China 2 Computers and Fluids 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Engineering 2 Journal of Approximation Theory 2 Proceedings of the American Mathematical Society 2 Systems & Control Letters 2 Acta Mathematicae Applicatae Sinica. English Series 2 Automation and Remote Control 2 European Journal of Operational Research 2 Celestial Mechanics and Dynamical Astronomy 2 Computational Optimization and Applications 2 Journal of Mathematical Sciences (New York) 2 ELA. 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)