×
Author ID: li.rencang Recent zbMATH articles by "Li, Rencang"
Published as: Li, Ren-Cang; Li, Rencang; Li, RenCang; Li, Ren-cang

Publications by Year

Citations contained in zbMATH Open

110 Publications have been cited 1,140 times in 674 Documents Cited by Year
On the ADI method for Sylvester equations. Zbl 1176.65050
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav
85
2009
Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010
Li, Ren-Cang
53
1998
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
46
2008
Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009
Li, Ren-Cang
39
1998
Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102
Bai, Zhaojun; Li, Ren-Cang
32
2013
Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
31
2012
Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078
Bai, Zhaojun; Li, Ren-Cang
30
2012
Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
27
2012
New perturbation bounds for the unitary polar factor. Zbl 0817.15012
Li, Ren-Cang
26
1995
Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060
Kahan, William; Li, Ren-Cang
26
1997
A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027
Li, Chi-Kwong; Li, Ren-Cang
24
2005
A Krylov subspace method for quadratic matrix polynomials with application to constrained least squares problems. Zbl 1050.65038
Li, Ren-Cang; Ye, Qiang
21
2003
On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036
Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang
20
2018
On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008
Li, Ren-Cang
19
2003
Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028
Li, Ren-Cang; Bai, Zhaojun
19
2005
A perturbation bound for the generalized polar decomposition. Zbl 0785.15007
Li, Ren-Cang
18
1993
Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073
Li, Ren-Cang; Zhang, Lei-Hong
18
2015
Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128
Zhang, LeiHong; Li, RenCang
18
2014
On perturbations of matrix pencils with real spectra. Zbl 0795.15012
Li, Ren-Cang
17
1994
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 1516.15006
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
17
2020
Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022
Zhou, Yunkai; Li, Ren-Cang
16
2011
Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102
Zhang, Leihong; Li, Rencang
15
2015
Krylov type subspace methods for matrix polynomials. Zbl 1104.65032
Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang
14
2006
On the generalized Lanczos trust-region method. Zbl 1380.90210
Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang
14
2017
Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010
Liang, Xin; Li, Ren-Cang; Bai, Zhaojun
14
2013
Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
13
2012
A perturbation bound for definite pencils. Zbl 0813.15017
Li, Ren-Cang
13
1993
Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018
Li, Ren-Cang
13
1997
Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011
Li, Ren-Cang
13
1997
Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. Zbl 0770.15009
Li, Rencang
13
1993
A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017
Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang
13
1996
Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006
Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei
13
2018
Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053
Li, Ren-Cang
12
2015
On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027
Li, Ren-Cang
11
2008
Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038
Chang, Xiao-Wen; Li, Ren-Cang
11
2011
Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053
Bai, Zhaojun; Li, Ren-Cang
11
2014
A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018
Li, Ren-Cang
10
1999
Bounds on perturbations of generalized singular values and of associated subspaces. Zbl 0771.15002
Li, Ren-Cang
10
1993
The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033
Liang, Xin; Li, Ren-Cang
10
2015
Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040
Teng, Zhongming; Li, Ren-Cang
10
2013
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
9
1996
Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021
Bai, ZhaoJun; Li, RenCang; Lin, WenWei
9
2016
Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049
Xue, Jungong; Li, Ren-Cang
9
2017
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
9
2019
QR decomposition and nonlinear eigenvalue problems. Zbl 0997.65527
Li, Rencang
8
1989
On eigenvalues of a Rayleigh quotient matrix. Zbl 0761.15006
Li, Rencang
8
1992
Pinchings and norms of scaled triangular matrices. Zbl 1004.15020
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang
8
2002
Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063
Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh
8
2010
Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang
7
2011
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
7
1997
A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046
Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang
7
2016
Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132
Li, Ren-Cang
7
2010
Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025
Li, Ren-Cang
6
2008
A new relative perturbation theorem for singular subspaces. Zbl 0962.15012
Li, Ren-Cang; Stewart, G. W.
6
2000
A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080
Li, Ren-Cang; Kahan, William
6
2012
Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036
Li, Ren-Cang
6
2004
Locally optimal and heavy ball GMRES methods. Zbl 1354.65063
Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang
6
2016
Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
6
2015
Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011
Li, Ren-Cang
5
2006
Spectral variations and Hadamard products: Some problems. Zbl 0933.15032
Li, Ren-Cang
5
1998
Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017
Li, Ren-Cang
5
2000
Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020
Li, Ren-Cang
5
2007
Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010
Li, Ren-Cang
5
2005
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016
Li, Ren-Cang; Zhang, Wei
5
2009
Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126
Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang
5
2014
Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015
Liang, Xin; Li, Ren-Cang
5
2014
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
5
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
5
2015
An interpolating family of means. Zbl 1331.26053
Bhatia, Rajendra; Li, Ren-Cang
5
2012
A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057
Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei
5
2017
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
5
2015
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
5
2010
Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. Zbl 1437.65022
Chen, Cairong; Li, Ren-Cang; Ma, Changfeng
5
2019
Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
5
2013
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
4
2007
On the variation of the spectra of matrix pencils. Zbl 0709.15010
Li, Rencang
4
1990
Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang
4
2007
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
4
2016
A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010
Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng
4
2008
A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057
Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang
4
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
4
2016
Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142
Bai, Zhaojun; Li, Ren-Cang; Lu, Ding
4
2022
Optimal parameters for doubling algorithms. Zbl 1413.65138
Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang
4
2017
A converse to the Bauer-Fike type theorem. Zbl 0655.15011
Li, Rencang
3
1988
Eigenvalues of symmetrizable matrices. Zbl 0898.15015
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
3
1998
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033
Li, Ren-Cang; Zhang, Wei
3
2009
A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028
Truhar, Ninoslav; Li, Ren-Cang
3
2003
Algorithms for inverse eigenvalue problems. Zbl 0751.65027
Li, Rencang
3
1992
Monotonicity of unitarily invariant norms. Zbl 1303.15029
Wang, Xue-Feng; Li, Ren-Cang
3
2015
Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071
Li, Ren-Cang; Ye, Qiang
3
2014
Hard cases for conjugate gradient method. Zbl 1156.65031
Li, Ren-Cang
3
2008
Orthogonal canonical correlation analysis and applications. Zbl 1455.65059
Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang
3
2020
On generalizing trace minimization principles. Zbl 1501.15005
Liang, Xin; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang
3
2023
On perturbation theorems for the generalized eigenvalues of regular matrix pairs. Zbl 0964.65504
Li, Rencang
2
1989
Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008
Li, Ren-Cang
2
2006
Perturbation bounds for generalized eigenvalues. I. Zbl 0693.15011
Li, Rencang
2
1989
The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048
Croot, Ernie; Li, Ren-Cang; Zhu, Hui June
2
2004
Solution of linear matrix equation \(AXD-BXC=S\) and perturbation of eigenspaces of a matrix pencil. Zbl 0793.15010
Li, Rencang
2
1992
Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035
Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang
2
2011
Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia
2
2016
On generalizing trace minimization principles. Zbl 1501.15005
Liang, Xin; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang
3
2023
Nearly optimal stochastic approximation for online principal subspace estimation. Zbl 1515.65027
Liang, Xin; Guo, Zhen-Chen; Wang, Li; Li, Ren-Cang; Lin, Wen-Wei
1
2023
Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142
Bai, Zhaojun; Li, Ren-Cang; Lu, Ding
4
2022
A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction. Zbl 1490.90213
Ma, Xijun; Shen, Chungen; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang
1
2022
Accurate numerical solution for structured \(M\)-matrix algebraic Riccati equations. Zbl 1470.65068
Liu, Changli; Wang, Wei-Guo; Xue, Jungong; Li, Ren-Cang
2
2021
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 1516.15006
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
17
2020
Orthogonal canonical correlation analysis and applications. Zbl 1455.65059
Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang
3
2020
Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations. Zbl 1445.65012
Liu, Changli; Xue, Jungong; Li, Ren-Cang
2
2020
Perturbation theory for Hermitian quadratic eigenvalue problem – damped and simultaneously diagonalizable systems. Zbl 1433.15019
Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang
1
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
9
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
5
2019
On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036
Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang
20
2018
Structure-preserving doubling algorithms for nonlinear matrix equations. Zbl 1435.65006
Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei
13
2018
On the generalized Lanczos trust-region method. Zbl 1380.90210
Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang
14
2017
Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. Zbl 1362.65049
Xue, Jungong; Li, Ren-Cang
9
2017
A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems. Zbl 1359.65057
Li, Tiexiang; Li, Ren-Cang; Lin, Wen-Wei
5
2017
Optimal parameters for doubling algorithms. Zbl 1413.65138
Huang, Tsungming; Li, Rencang; Lin, Wenwei; Lu, Linzhang
4
2017
Error bounds for approximate deflating subspaces for linear response eigenvalue problems. Zbl 1398.15016
Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang
1
2017
Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021
Bai, ZhaoJun; Li, RenCang; Lin, WenWei
9
2016
A block Chebyshev-Davidson method for linear response eigenvalue problems. Zbl 1357.65046
Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang
7
2016
Locally optimal and heavy ball GMRES methods. Zbl 1354.65063
Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang
6
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
4
2016
A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057
Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang
4
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
4
2016
Self-corrective iterations (SCI) for generalized diagonally dominant matrices. Zbl 1334.15096
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia
2
2016
Convergence of the block Lanczos method for eigenvalue clusters. Zbl 1334.65073
Li, Ren-Cang; Zhang, Lei-Hong
18
2015
Maximization of the sum of the trace ratio on the Stiefel manifold. II: computation. Zbl 1384.90102
Zhang, Leihong; Li, Rencang
15
2015
Rayleigh quotient based optimization methods for eigenvalue problems. Zbl 1332.65053
Li, Ren-Cang
12
2015
The hyperbolic quadratic eigenvalue problem. Zbl 1328.15033
Liang, Xin; Li, Ren-Cang
10
2015
Cluster-robust accuracy bounds for Ritz subspaces. Zbl 1320.15013
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
6
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
5
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
5
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
5
2015
Monotonicity of unitarily invariant norms. Zbl 1303.15029
Wang, Xue-Feng; Li, Ren-Cang
3
2015
Perturbation of partitioned linear response eigenvalue problems. Zbl 1330.65060
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang
1
2015
Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. Zbl 1341.90128
Zhang, LeiHong; Li, RenCang
18
2014
Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053
Bai, Zhaojun; Li, Ren-Cang
11
2014
Rayleigh-Ritz approximation for the linear response eigenvalue problem. Zbl 1305.65126
Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang
5
2014
Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Zbl 1307.15015
Liang, Xin; Li, Ren-Cang
5
2014
Simultaneous similarity reductions for a pair of matrices to condensed forms. Zbl 1312.65071
Li, Ren-Cang; Ye, Qiang
3
2014
GIP integrators for matrix Riccati differential equations. Zbl 1337.65074
Kristopher Garrett, C.; Li, Ren-Cang
2
2014
Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102
Bai, Zhaojun; Li, Ren-Cang
32
2013
Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010
Liang, Xin; Li, Ren-Cang; Bai, Zhaojun
14
2013
Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem. Zbl 1279.65040
Teng, Zhongming; Li, Ren-Cang
10
2013
Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. Zbl 1271.15005
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
5
2013
Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. Zbl 1258.65045
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang
31
2012
Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078
Bai, Zhaojun; Li, Ren-Cang
30
2012
Accurate solutions of \(M\)-matrix algebraic Riccati equations. Zbl 1260.15025
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
27
2012
Accurate solutions of \(M\)-matrix Sylvester equations. Zbl 1245.65053
Xue, Jungong; Xu, Shufang; Li, Ren-Cang
13
2012
A family of anadromic numerical methods for matrix Riccati differential equations. Zbl 1236.65080
Li, Ren-Cang; Kahan, William
6
2012
An interpolating family of means. Zbl 1331.26053
Bhatia, Rajendra; Li, Ren-Cang
5
2012
Perturbation of multiple eigenvalues of Hermitian matrices. Zbl 1242.15016
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Wang, Wei-Guo
1
2012
Bounding the spectrum of large Hermitian matrices. Zbl 1221.15022
Zhou, Yunkai; Li, Ren-Cang
16
2011
Multiplicative perturbation analysis for QR factorizations. Zbl 1247.65038
Chang, Xiao-Wen; Li, Ren-Cang
11
2011
Perturbation of partitioned Hermitian definite generalized eigenvalue problems. Zbl 1230.15011
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang
7
2011
Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035
Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang
2
2011
Structured backward error for palindromic polynomial eigenvalue problems. Zbl 1213.65063
Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh
8
2010
Sharpness in rates of convergence for the symmetric Lanczos method. Zbl 1206.65132
Li, Ren-Cang
7
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
5
2010
On the ADI method for Sylvester equations. Zbl 1176.65050
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav
85
2009
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. Zbl 1162.65016
Li, Ren-Cang; Zhang, Wei
5
2009
The rate of convergence of GMRES on a tridiagonal Toeplitz linear system. II. Zbl 1178.65033
Li, Ren-Cang; Zhang, Wei
3
2009
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
46
2008
On Meinardus’ examples for the conjugate gradient method. Zbl 1128.65027
Li, Ren-Cang
11
2008
Vandermonde matrices with Chebyshev nodes. Zbl 1140.65025
Li, Ren-Cang
6
2008
A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010
Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng
4
2008
Hard cases for conjugate gradient method. Zbl 1156.65031
Li, Ren-Cang
3
2008
Convergence of CG and GMRES on a tridiagonal Toeplitz linear system. Zbl 1129.65020
Li, Ren-Cang
5
2007
Eigenvalues of an alignment matrix in nonlinear manifold learning. Zbl 1135.65019
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang
4
2007
Analysis of an alignment algorithm for nonlinear dimensionality reduction. Zbl 1129.62062
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang
4
2007
Krylov type subspace methods for matrix polynomials. Zbl 1104.65032
Hoffnung, Leonard; Li, Ren-Cang; Ye, Qiang
14
2006
Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. Zbl 1125.15011
Li, Ren-Cang
5
2006
Lower bounds for the condition number of a real confluent Vandermonde matrix. Zbl 1119.15008
Li, Ren-Cang
2
2006
A note on eigenvalues of perturbed Hermitian matrices. Zbl 1068.15027
Li, Chi-Kwong; Li, Ren-Cang
24
2005
Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028
Li, Ren-Cang; Bai, Zhaojun
19
2005
Relative perturbation bounds for positive polar factors of graded matrices. Zbl 1099.15010
Li, Ren-Cang
5
2005
Accuracy of computed eigenvectors via optimizing a Rayleigh quotient. Zbl 1069.65036
Li, Ren-Cang
6
2004
The \(abc\) conjecture and correctly rounded reciprocal square roots. Zbl 1060.65048
Croot, 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 1050.65038
Li, Ren-Cang; Ye, Qiang
21
2003
On perturbations of matrix pencils with real spectra, a revisit. Zbl 1047.15008
Li, Ren-Cang
19
2003
A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. Zbl 1025.15028
Truhar, Ninoslav; Li, Ren-Cang
3
2003
Pinchings and norms of scaled triangular matrices. Zbl 1004.15020
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang
8
2002
A new relative perturbation theorem for singular subspaces. Zbl 0962.15012
Li, Ren-Cang; Stewart, G. W.
6
2000
Relative perturbation theory. IV: \(\sin 2\theta\) theorems. Zbl 0963.15017
Li, Ren-Cang
5
2000
A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. Zbl 0964.15018
Li, Ren-Cang
10
1999
Relative perturbation theory. II: Eigenspace and singular subspace variations. Zbl 0917.15010
Li, Ren-Cang
53
1998
Relative perturbation theory. I: Eigenvalue and singular value variations. Zbl 0917.15009
Li, Ren-Cang
39
1998
Spectral variations and Hadamard products: Some problems. Zbl 0933.15032
Li, Ren-Cang
5
1998
Eigenvalues of symmetrizable matrices. Zbl 0898.15015
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
3
1998
Composition constants for raising the orders of unconventional schemes for ordinary differential equations. Zbl 0870.65060
Kahan, William; Li, Ren-Cang
26
1997
Relative perturbation bounds for the unitary polar factor. Zbl 0871.15018
Li, Ren-Cang
13
1997
Relative perturbation theory. III: More bounds on eigenvalue variation. Zbl 0917.15011
Li, Ren-Cang
13
1997
Some inequalities for commutators and an application to spectral variation. II. Zbl 0901.47012
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang
7
1997
A sharp version of Kahan’s theorem on clustered eigenvalues. Zbl 0860.15017
Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang
13
1996
On perturbations of matrix pencils with real spectra. II. Zbl 0852.15008
Bhatia, Rajendra; Li, Ren-Cang
9
1996
New perturbation bounds for the unitary polar factor. Zbl 0817.15012
Li, Ren-Cang
26
1995
On perturbations of matrix pencils with real spectra. Zbl 0795.15012
Li, Ren-Cang
17
1994
A perturbation bound for the generalized polar decomposition. Zbl 0785.15007
Li, Ren-Cang
18
1993
A perturbation bound for definite pencils. Zbl 0813.15017
Li, Ren-Cang
13
1993
Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. Zbl 0770.15009
Li, Rencang
13
1993
...and 10 more Documents
all top 5

Cited by 882 Authors

69 Li, Rencang
23 Zhang, Lei-Hong
22 Benner, Peter
17 Li, Wen
16 Truhar, Ninoslav
14 Dopico, Froilán M.
12 Bai, Zhaojun
12 Li, Hanyu
12 Shen, Chungen
10 Liang, Xin
10 Nakatsukasa, Yuji
10 Reichel, Lothar
10 Wang, Xiang
10 Wei, Yimin
9 Kressner, Daniel
9 Lin, Wen-Wei
9 Ma, Changfeng
9 Ye, Qiang
8 Chen, Xiaoshan
8 Kürschner, Patrick
7 Chen, Xiaoping
7 Dai, Hua
7 Saak, Jens
7 Townsend, Alex
7 Yang, Chao
7 Yang, Weihong
6 Blanes, Sergio
6 Chen, Hongjia
6 Kittaneh, Fuad
6 Lawrence, Piers W.
6 Su, Yangfeng
6 Tisseur, Françoise
6 Wang, Weiguo
6 Wei, Wei
6 Yang, Hu
6 Zheng, Bing
5 Bhatia, Rajendra
5 Huang, Tsungming
5 Lu, Ding
5 Meng, Lingsheng
5 Miodragović, Suzana
5 Rehman, Abdur
5 Saad, Yousef
5 Simoncini, Valeria
5 Slapničar, Ivan
5 Stykel, Tatjana
5 Teng, Zhongming
5 Wang, Li
5 Wang, Qingwen
5 Xi, Yuanzhe
5 Xu, Wei-Wei
5 Xue, Jungong
5 Zhou, Yunkai
4 Beik, Fatemeh Panjeh Ali
4 Casas, Fernando
4 de Terán, Fernando
4 Grubišić, Luka
4 Guo, Chun-Hua
4 Guo, Zhen-chen
4 Hochstenbach, Michiel E.
4 Huang, Na
4 Ipsen, Ilse C. F.
4 Jarlebring, Elias
4 Kuo, Yueh-Cheng
4 Kyrchei, Ivan I.
4 Li, Jicheng
4 Li, Tiexiang
4 Lu, Linzhang
4 Palitta, Davide
4 Samar, Mahvish
4 Shao, Meiyue
4 Tomljanović, Zoran
4 Van Dooren, Paul M.
4 Wen, Zaiwen
4 Xu, Qingxiang
3 Beckermann, Bernhard
3 Chen, Cairong
3 Chiang, Chun-Yueh
3 Chu, Delin
3 Corless, Robert Malcolm
3 Cucuringu, Mihai
3 Dolgov, Sergey V.
3 Dong, Liqiang
3 Dong, Ning
3 Doostaki, Reza
3 Drmač, Zlatko
3 Du, Lei
3 Farooq, Aamir
3 Ferreira, Carla
3 Fu, Chunhong
3 Furtado, Susana
3 Huang, Weiqiang
3 Imakura, Akira
3 Jbilou, Khalide
3 Jia, Lu
3 Jia, Zhongxiao
3 Khoromskiĭ, Boris Nikolaevich
3 King-wah Chu, Eric
3 Li, Chi-Kwong
3 Li, Yung-Ta
...and 782 more Authors
all top 5

Cited in 165 Serials

97 Linear Algebra and its Applications
44 SIAM Journal on Matrix Analysis and Applications
29 Journal of Computational and Applied Mathematics
26 SIAM Journal on Scientific Computing
25 Numerische Mathematik
24 Linear and Multilinear Algebra
24 BIT
23 Applied Mathematics and Computation
18 Numerical Algorithms
16 Journal of Scientific Computing
15 Applied Numerical Mathematics
14 Mathematics of Computation
13 Numerical Linear Algebra with Applications
12 Computers & Mathematics with Applications
10 Journal of Computational Physics
9 Calcolo
9 International Journal of Computer Mathematics
9 SIAM Journal on Optimization
8 Computational and Applied Mathematics
7 East Asian Journal on Applied Mathematics
6 ETNA. Electronic Transactions on Numerical Analysis
5 Journal of the Franklin Institute
5 Applied Mathematics Letters
5 SIAM Review
5 Filomat
5 Journal of Machine Learning Research (JMLR)
5 Science China. Mathematics
4 SIAM Journal on Numerical Analysis
4 Advances in Computational Mathematics
4 ELA. The Electronic Journal of Linear Algebra
4 Numerical Algebra, Control and Optimization
3 Computer Methods in Applied Mechanics and Engineering
3 Computer Physics Communications
3 Journal of Mathematical Analysis and Applications
3 ACM Transactions on Mathematical Software
3 Automatica
3 Japan Journal of Industrial and Applied Mathematics
3 Applied and Computational Harmonic Analysis
3 Optimization Methods & Software
3 Taiwanese Journal of Mathematics
3 Acta Mathematica Sinica. English Series
3 Computational Methods in Applied Mathematics
3 Journal of Applied Mathematics and Computing
3 Frontiers of Mathematics in China
2 Computers and Fluids
2 Indian Journal of Pure & Applied Mathematics
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 Applied Mathematical Modelling
2 Automation and Remote Control
2 European Journal of Operational Research
2 Mathematical Programming. Series A. Series B
2 Celestial Mechanics and Dynamical Astronomy
2 Computational Optimization and Applications
2 Journal of Mathematical Sciences (New York)
2 Advances in Applied Clifford Algebras
2 Mathematical Problems in Engineering
2 Mathematical Inequalities & Applications
2 Foundations of Computational Mathematics
2 Stochastic Models
2 SIAM Journal on Applied Dynamical Systems
2 Communications on Applied Mathematics and Computation
2 Electronic Research Archive
1 American Mathematical Monthly
1 Archive for Rational Mechanics and Analysis
1 Inverse Problems
1 Journal of Engineering Mathematics
1 Physica A
1 Arkiv för Matematik
1 Chaos, Solitons and Fractals
1 Demonstratio Mathematica
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 Mathematics of Operations Research
1 Mathematische Zeitschrift
1 Numerical Functional Analysis and Optimization
1 Theoretical Computer Science
1 Journal of Computational Mathematics
1 Optimization
1 Algorithmica
1 Mathematical and Computer Modelling
1 Queueing Systems
1 Science in China. Series A
1 Annals of Operations Research
1 Machine Learning
1 Applications of Mathematics
1 Aequationes Mathematicae
1 Glasnik Matematički. Serija III
1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1 Computational Statistics and Data Analysis
1 Journal of Mathematical Imaging and Vision
1 Algebra Colloquium
1 Bulletin of the Belgian Mathematical Society - Simon Stevin
1 Journal of Inverse and Ill-Posed Problems
...and 65 more Serials
all top 5

Cited in 39 Fields

491 Numerical analysis (65-XX)
368 Linear and multilinear algebra; matrix theory (15-XX)
60 Operations research, mathematical programming (90-XX)
48 Operator theory (47-XX)
41 Systems theory; control (93-XX)
30 Computer science (68-XX)
25 Partial differential equations (35-XX)
23 Ordinary differential equations (34-XX)
14 Calculus of variations and optimal control; optimization (49-XX)
13 Dynamical systems and ergodic theory (37-XX)
13 Probability theory and stochastic processes (60-XX)
11 Combinatorics (05-XX)
10 Mechanics of particles and systems (70-XX)
10 Fluid mechanics (76-XX)
10 Quantum theory (81-XX)
8 Real functions (26-XX)
8 Functions of a complex variable (30-XX)
8 Information and communication theory, circuits (94-XX)
7 Statistics (62-XX)
6 Special functions (33-XX)
6 Approximations and expansions (41-XX)
6 Mechanics of deformable solids (74-XX)
6 Biology and other natural sciences (92-XX)
5 Statistical mechanics, structure of matter (82-XX)
4 Difference and functional equations (39-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
3 Optics, electromagnetic theory (78-XX)
2 Number theory (11-XX)
2 Nonassociative rings and algebras (17-XX)
2 Differential geometry (53-XX)
2 General topology (54-XX)
2 Classical thermodynamics, heat transfer (80-XX)
2 Astronomy and astrophysics (85-XX)
1 Measure and integration (28-XX)
1 Sequences, series, summability (40-XX)
1 Functional analysis (46-XX)
1 Convex and discrete geometry (52-XX)
1 Geophysics (86-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

Citations by Year