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## Li, Rencang

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 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
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#### 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
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#### 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
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#### 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)

#### 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 1176.65050
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
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
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
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
Alternating-directional doubling algorithm for $$M$$-matrix algebraic Riccati equations. Zbl 1258.65045
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
2012
Accurate solutions of $$M$$-matrix algebraic Riccati equations. Zbl 1260.15025
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
2012
A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038
Li, Ren-Cang; Ye, Qiang
2003
New perturbation bounds for the unitary polar factor. Zbl 0817.15012
Li, Ren-Cang
1995
On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008
Li, Ren-Cang
2003
A perturbation bound for the generalized polar decomposition. Zbl 0785.15007
Li, Ren-Cang
1993
On perturbations of matrix pencils with real spectra. Zbl 0795.15012
Li, Ren-Cang
1994
Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011
Li, Ren-Cang
1997
A perturbation bound for definite pencils. Zbl 0813.15017
Li, Ren-Cang
1993
Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022
Zhou, Yunkai; Li, Ren-Cang
2011
Krylov type subspace methods for matrix polynomials. Zbl 1104.65032
Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang
2006
Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028
Li, Ren-Cang; Bai, Zhaojun
2005
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
Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073
Li, Ren-Cang; Zhang, Lei-Hong
2015
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
Accurate solutions of $$M$$-matrix Sylvester equations. Zbl 1245.65053
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
2012
Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040
Teng, Zhongming; Li, Ren-Cang
2013
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
1996
Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102
Zhang, Leihong; Li, Rencang
2015
Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128
Zhang, LeiHong; Li, RenCang
2014
Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010
Liang, Xin; Li, Ren-Cang; Bai, Zhaojun
2013
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
Bounds on perturbations of generalized singular values and of associated subspaces. Zbl 0771.15002
Li, Ren-Cang
1993
On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006
Li, Rencang
1992
On the generalized Lanczos trust-region method. Zbl 1380.90210
Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang
2017
Cooperative enclosing control for multiple moving targets by a group of agents. Zbl 1328.93033
Shi, Y. J.; Li, R.; Teo, K. L.
2015
Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053
Bai, Zhaojun; Li, Ren-Cang
2014
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
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1997
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
A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046
Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang
2016
Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026
Shi, Y. J.; Li, R.; Wei, T. T.
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
Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126
Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang
2014
A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080
Li, Ren-Cang; Kahan, William
2012
Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132
Li, Ren-Cang
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
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016
Li, Ren-Cang; Zhang, Wei
2009
Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025
Li, Ren-Cang
2008
Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020
Li, Ren-Cang
2007
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
An Orlicz-Pettis theorem with applications to $$\mathcal A$$-spaces. Zbl 1012.46003
Wu, Jun De; Li, R.
1999
A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018
Li, Ren-Cang
1999
Spectral variations and Hadamard products: Some problems. Zbl 0933.15032
Li, Ren-Cang
1998
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
The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033
Liang, Xin; Li, Ren-Cang
2015
Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
2015
Deflating irreducible singular $$M$$-matrix Algebraic Riccati Equations. Zbl 1271.15005
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
2013
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
2007
Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang
2007
Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011
Li, Ren-Cang
2006
Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010
Li, Ren-Cang
2005
On the variation of the spectra of matrix pencils. Zbl 0709.15010
Li, Rencang
1990
On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036
Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang
2018
Locally optimal and heavy ball GMRES methods. Zbl 1354.65063
Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang
2016
Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021
Bai, ZhaoJun; Li, RenCang; Lin, WenWei
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 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 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
Monotonicity of unitarily invariant norms. Zbl 1303.15029
Wang, Xue-Feng; Li, Ren-Cang
2015
An interpolating family of means. Zbl 1331.26053
Bhatia, Rajendra; Li, Ren-Cang
2012
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033
Li, Ren-Cang; Zhang, Wei
2009
Hard cases for conjugate gradient method. Zbl 1156.65031
Li, Ren-Cang
2008
Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036
Li, Ren-Cang
2004
A $$\sin 2\varTheta$$ theorem for graded indefinite Hermitian matrices. Zbl 1025.15028
Truhar, Ninoslav; Li, Ren-Cang
2003
Eigenvalues of symmetrizable matrices. Zbl 0898.15015
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
1998
QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527
Li, Rencang
1989
On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504
Li, Rencang
1989
A converse to the Bauer-Fike type theorem. Zbl 0655.15011
Li, Rencang
1988
A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057
Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang
2016
Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291
Wen, M.; Li, R.; Salling, K. B.
2016
Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia
2016
Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053
Li, Ren-Cang
2015
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
A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010
Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng
2008
The $$abc$$ conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048
Croot, Ernie; Li, Ren-Cang; Zhu, Hui June
2004
Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011
Li, Rencang
1989
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
2020
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
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
Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006
Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei
2018
Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016
Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang
2017
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
2020
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
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
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
Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016
Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang
2017
Optimal parameters for doubling algorithms. Zbl 1413.65138
Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang
2017
A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046
Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang
2016
Locally optimal and heavy ball GMRES methods. Zbl 1354.65063
Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang
2016
Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021
Bai, ZhaoJun; Li, RenCang; Lin, WenWei
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 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 nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057
Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang
2016
Optimization of preventive condition-based tamping for railway tracks. Zbl 1346.90291
Wen, M.; Li, R.; Salling, K. B.
2016
Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia
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
Target-enclosing control for second-order multi-agent systems. Zbl 1332.93026
Shi, Y. J.; Li, R.; Wei, T. T.
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
The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033
Liang, Xin; Li, Ren-Cang
2015
Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
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
Monotonicity of unitarily invariant norms. Zbl 1303.15029
Wang, Xue-Feng; Li, Ren-Cang
2015
Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053
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
Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078
Bai, Zhaojun; Li, Ren-Cang
2012
Alternating-directional doubling algorithm for $$M$$-matrix algebraic Riccati equations. Zbl 1258.65045
Wang, Wei-Guo; Wang, Wei-Chao; 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
Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132
Li, Ren-Cang
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
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
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
2007
Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang
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
An Orlicz-Pettis theorem with applications to $$\mathcal A$$-spaces. Zbl 1012.46003
Wu, Jun De; Li, R.
1999
A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018
Li, Ren-Cang
1999
Hypocontinuity and uniform boundedness for bilinear maps. Zbl 0938.47046
Wu, Jun De; Li, R.
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
A perturbation bound for definite pencils. Zbl 0813.15017
Li, Ren-Cang
1993
...and 10 more Documents
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#### 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
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#### 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. Electronic Transactions on Numerical Analysis 5 Science China. Mathematics 5 East Asian Journal on Applied Mathematics 4 Journal of Mathematical Analysis and Applications 4 Mathematical and Computer Modelling 4 European Journal of Operational Research 4 Journal of Industrial and Management Optimization 4 Numerical Algebra, Control and Optimization 3 Journal of the Franklin Institute 3 Proceedings of the American Mathematical Society 3 Applied Mathematics Letters 3 Applied Mathematical Modelling 3 Advances in Computational Mathematics 3 Nonlinear Dynamics 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 Journal of Optimization Theory and Applications 2 SIAM Journal on Numerical Analysis 2 Systems & Control Letters 2 Acta Mathematicae Applicatae Sinica. English Series 2 Science in China. Series A 2 Japan Journal of Industrial and Applied Mathematics 2 Automation and Remote Control 2 Celestial Mechanics and Dynamical Astronomy 2 Journal of Mathematical Sciences (New York) 2 Abstract and Applied Analysis 2 Taiwanese Journal of Mathematics 2 Mathematical Inequalities & Applications 2 Acta Mathematica Sinica. English Series 2 The ANZIAM Journal 2 Stochastic Models 2 Nonlinear Analysis. Hybrid Systems 2 Journal of the Operations Research Society of China 2 International Journal of Systems Science. 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
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#### 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)