Liang, Xin; Li, Ren-Cang On generalizing trace minimization principles. II. (English) Zbl 07810689 Linear Algebra Appl. 687, 8-37 (2024). MSC: 15A15 15A22 15B57 PDFBibTeX XMLCite \textit{X. Liang} and \textit{R.-C. Li}, Linear Algebra Appl. 687, 8--37 (2024; Zbl 07810689) Full Text: DOI arXiv
Karaduman, Gul; Yang, Mei; Li, Ren-Cang A least squares approach for saddle point problems. (English) Zbl 1505.65159 Japan J. Ind. Appl. Math. 40, No. 1, 95-107 (2023). MSC: 65F10 65F20 65F25 65F35 65F50 15A06 PDFBibTeX XMLCite \textit{G. Karaduman} et al., Japan J. Ind. Appl. Math. 40, No. 1, 95--107 (2023; Zbl 1505.65159) Full Text: DOI
Liang, Xin; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang On generalizing trace minimization principles. (English) Zbl 1501.15005 Linear Algebra Appl. 656, 483-509 (2023). MSC: 15A15 15A18 15A22 65F15 90C20 90C26 PDFBibTeX XMLCite \textit{X. Liang} et al., Linear Algebra Appl. 656, 483--509 (2023; Zbl 1501.15005) Full Text: DOI
Teng, Zhongming; Li, Ren-Cang Variations of Orthonormal Basis Matrices of Subspaces. arXiv:2304.00304 Preprint, arXiv:2304.00304 [math.NA] (2023). MSC: 15A45 65F35 BibTeX Cite \textit{Z. Teng} and \textit{R.-C. Li}, ``Variations of Orthonormal Basis Matrices of Subspaces'', Preprint, arXiv:2304.00304 [math.NA] (2023) Full Text: arXiv OA License
Liu, Changli; Xue, Jungong; Li, Ren-Cang On nonlinear matrix equations from the first standard form. (English) Zbl 1502.65019 Ann. Math. Sci. Appl. 7, No. 2, 169-191 (2022). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{C. Liu} et al., Ann. Math. Sci. Appl. 7, No. 2, 169--191 (2022; Zbl 1502.65019) Full Text: DOI
Gu, Guiding; Li, Wang; Li, Ren-Cang Highly accurate Latouche-Ramaswami logarithmic reduction algorithm for quasi-birth-and-death process. (English) Zbl 1499.65143 J. Math. Study 55, No. 2, 180-194 (2022). MSC: 65F45 15A24 65H10 PDFBibTeX XMLCite \textit{G. Gu} et al., J. Math. Study 55, No. 2, 180--194 (2022; Zbl 1499.65143) Full Text: DOI
Liu, Changli; Wang, Wei-Guo; Xue, Jungong; Li, Ren-Cang Accurate numerical solution for structured \(M\)-matrix algebraic Riccati equations. (English) Zbl 1470.65068 J. Comput. Appl. Math. 396, Article ID 113614, 16 p. (2021). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Appl. Math. 396, Article ID 113614, 16 p. (2021; Zbl 1470.65068) Full Text: DOI
Truhar, Ninoslav; Li, Ren-Cang On an eigenvector-dependent nonlinear eigenvalue problem from the perspective of relative perturbation theory. (English) Zbl 1473.15018 J. Comput. Appl. Math. 395, Article ID 113596, 11 p. (2021). Reviewer: Manouchehr Misaghian (Prairie View) MSC: 15A18 65F15 65H17 47J10 47H09 PDFBibTeX XMLCite \textit{N. Truhar} and \textit{R.-C. Li}, J. Comput. Appl. Math. 395, Article ID 113596, 11 p. (2021; Zbl 1473.15018) Full Text: DOI
Liang, Xin; Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang On Generalizing Trace Minimization. arXiv:2104.00257 Preprint, arXiv:2104.00257 [math.NA] (2021). MSC: 15A18 15A22 65F15 BibTeX Cite \textit{X. Liang} et al., ``On Generalizing Trace Minimization'', Preprint, arXiv:2104.00257 [math.NA] (2021) Full Text: DOI arXiv OA License
Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang Orthogonal canonical correlation analysis and applications. (English) Zbl 1455.65059 Optim. Methods Softw. 35, No. 4, 787-807 (2020). MSC: 65F15 15A18 65K05 90C90 PDFBibTeX XMLCite \textit{L. Wang} et al., Optim. Methods Softw. 35, No. 4, 787--807 (2020; Zbl 1455.65059) Full Text: DOI
Liu, Changli; Xue, Jungong; Li, Ren-Cang Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations. (English) Zbl 1445.65012 J. Sci. Comput. 84, No. 1, Paper No. 15, 27 p. (2020). MSC: 65F45 15A24 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Sci. Comput. 84, No. 1, Paper No. 15, 27 p. (2020; Zbl 1445.65012) Full Text: DOI
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L. First-order perturbation theory for eigenvalues and eigenvectors. (English) Zbl 1516.15006 SIAM Rev. 62, No. 2, 463-482 (2020). MSC: 15A18 65F15 15A60 47A55 PDFBibTeX XMLCite \textit{A. Greenbaum} et al., SIAM Rev. 62, No. 2, 463--482 (2020; Zbl 1516.15006) Full Text: DOI arXiv
Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang Perturbation theory for Hermitian quadratic eigenvalue problem – damped and simultaneously diagonalizable systems. (English) Zbl 1433.15019 Appl. Math. Comput. 371, Article ID 124921, 17 p. (2020). MSC: 15A22 15A18 47H14 65F15 PDFBibTeX XMLCite \textit{N. Truhar} et al., Appl. Math. Comput. 371, Article ID 124921, 17 p. (2020; Zbl 1433.15019) Full Text: DOI
Chen, Cairong; Li, Ren-Cang; Ma, Changfeng Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process. (English) Zbl 1437.65022 Linear Algebra Appl. 583, 1-45 (2019). MSC: 65F45 15A24 65H10 PDFBibTeX XMLCite \textit{C. Chen} et al., Linear Algebra Appl. 583, 1--45 (2019; Zbl 1437.65022) Full Text: DOI
Cai, Yunfeng; Li, Ren-Cang Perturbation analysis for matrix joint block diagonalization. (English) Zbl 1437.15015 Linear Algebra Appl. 581, 163-197 (2019). MSC: 15A20 15A21 PDFBibTeX XMLCite \textit{Y. Cai} and \textit{R.-C. Li}, Linear Algebra Appl. 581, 163--197 (2019; Zbl 1437.15015) Full Text: DOI arXiv
Huang, Tsung-Ming; Li, Ren-Cang; Lin, Wen-Wei Structure-preserving doubling algorithms for nonlinear matrix equations. (English) Zbl 1435.65006 Fundamentals of Algorithms 14. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-535-2/pbk; 978-1-61197-536-9/ebook). xii, 144 p. (2018). Reviewer: Adhemar Bultheel (Leuven) MSC: 65-02 65F45 65F15 15A24 PDFBibTeX XMLCite \textit{T.-M. Huang} et al., Structure-preserving doubling algorithms for nonlinear matrix equations. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2018; Zbl 1435.65006) Full Text: DOI
Wang, Wei-Guo; Zhang, Lei-Hong; Li, Ren-Cang Error bounds for approximate deflating subspaces for linear response eigenvalue problems. (English) Zbl 1398.15016 Linear Algebra Appl. 528, 273-289 (2017). MSC: 15A42 65F15 PDFBibTeX XMLCite \textit{W.-G. Wang} et al., Linear Algebra Appl. 528, 273--289 (2017; Zbl 1398.15016) Full Text: DOI
Xue, Jungong; Li, Ren-Cang Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations. (English) Zbl 1362.65049 Numer. Math. 135, No. 3, 733-767 (2017). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{J. Xue} and \textit{R.-C. Li}, Numer. Math. 135, No. 3, 733--767 (2017; Zbl 1362.65049) Full Text: DOI
Yuan, Fei; Lu, Linzhang; Li, Rencang Backward error analysis for some quadratic eigenvalue problems. (Chinese. English summary) Zbl 1363.15017 J. Xiamen Univ., Nat. Sci. 55, No. 1, 97-102 (2016). MSC: 15A18 15A24 PDFBibTeX XMLCite \textit{F. Yuan} et al., J. Xiamen Univ., Nat. Sci. 55, No. 1, 97--102 (2016; Zbl 1363.15017) Full Text: DOI
Huang, Tsung-Ming; Huang, Wei-Qiang; Li, Ren-Cang; Lin, Wen-Wei A new two-phase structure-preserving doubling algorithm for critically singular \(M\)-matrix algebraic Riccati equations. (English) Zbl 1374.65068 Numer. Linear Algebra Appl. 23, No. 2, 291-313 (2016). Reviewer: Edgar Pereira (Natal) MSC: 65F30 15A24 65F10 PDFBibTeX XMLCite \textit{T.-M. Huang} et al., Numer. Linear Algebra Appl. 23, No. 2, 291--313 (2016; Zbl 1374.65068) Full Text: DOI
Guan, Jinrui; Lu, Linzhang; Li, Ren-Cang; Shao, Rongxia Self-corrective iterations (SCI) for generalized diagonally dominant matrices. (English) Zbl 1334.15096 J. Comput. Appl. Math. 302, 285-300 (2016). MSC: 15B99 15B52 65F10 65F35 PDFBibTeX XMLCite \textit{J. Guan} et al., J. Comput. Appl. Math. 302, 285--300 (2016; Zbl 1334.15096) Full Text: DOI
Lu, Linzhang; Yuan, Fei; Li, Ren-Cang A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem. (English) Zbl 1363.65097 Numer. Linear Algebra Appl. 22, No. 3, 393-409 (2015). Reviewer: Liu Xinguo (Qingdao) MSC: 65H17 65F15 15A24 PDFBibTeX XMLCite \textit{L. Lu} et al., Numer. Linear Algebra Appl. 22, No. 3, 393--409 (2015; Zbl 1363.65097) Full Text: DOI
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang Perturbation of partitioned linear response eigenvalue problems. (English) Zbl 1330.65060 ETNA, Electron. Trans. Numer. Anal. 44, 624-638 (2015). MSC: 65F15 15A42 PDFBibTeX XMLCite \textit{Z. Teng} et al., ETNA, Electron. Trans. Numer. Anal. 44, 624--638 (2015; Zbl 1330.65060) Full Text: EMIS
Liang, Xin; Li, Ren-Cang The hyperbolic quadratic eigenvalue problem. (English) Zbl 1328.15033 Forum Math. Sigma 3, Paper No. e13, 93 p. (2015). MSC: 15A42 65F15 15A18 65F08 65F50 65G99 PDFBibTeX XMLCite \textit{X. Liang} and \textit{R.-C. Li}, Forum Math. Sigma 3, Paper No. e13, 93 p. (2015; Zbl 1328.15033) Full Text: DOI
Teng, Zhongming; Lu, Linzhang; Li, Ren-Cang Cluster-robust accuracy bounds for Ritz subspaces. (English) Zbl 1320.15013 Linear Algebra Appl. 480, 11-26 (2015). MSC: 15A42 65F15 PDFBibTeX XMLCite \textit{Z. Teng} et al., Linear Algebra Appl. 480, 11--26 (2015; Zbl 1320.15013) Full Text: DOI
Wang, Xue-Feng; Li, Ren-Cang Monotonicity of unitarily invariant norms. (English) Zbl 1303.15029 Linear Algebra Appl. 466, 254-266 (2015). MSC: 15A60 15A18 PDFBibTeX XMLCite \textit{X.-F. Wang} and \textit{R.-C. Li}, Linear Algebra Appl. 466, 254--266 (2015; Zbl 1303.15029) Full Text: DOI
Kristopher Garrett, C.; Li, Ren-Cang GIP integrators for matrix Riccati differential equations. (English) Zbl 1337.65074 Appl. Math. Comput. 241, 283-297 (2014). MSC: 65L06 93C05 15A24 PDFBibTeX XMLCite \textit{C. Kristopher Garrett} and \textit{R.-C. Li}, Appl. Math. Comput. 241, 283--297 (2014; Zbl 1337.65074) Full Text: DOI
Zhang, LeiHong; Li, RenCang Maximization of the sum of the trace ratio on the Stiefel manifold. I: Theory. (English) Zbl 1341.90128 Sci. China, Math. 57, No. 12, 2495-2508 (2014). MSC: 90C32 90C46 65F15 65F30 62H30 15A18 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{R. Li}, Sci. China, Math. 57, No. 12, 2495--2508 (2014; Zbl 1341.90128) Full Text: DOI
Li, Ren-Cang; Ye, Qiang Simultaneous similarity reductions for a pair of matrices to condensed forms. (English) Zbl 1312.65071 Commun. Math. Stat. 2, No. 2, 139-153 (2014). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 15A21 PDFBibTeX XMLCite \textit{R.-C. Li} and \textit{Q. Ye}, Commun. Math. Stat. 2, No. 2, 139--153 (2014; Zbl 1312.65071) Full Text: DOI
Liang, Xin; Li, Ren-Cang Extensions of Wielandt’s min-max principles for positive semi-definite pencils. (English) Zbl 1307.15015 Linear Multilinear Algebra 62, No. 8, 1032-1048 (2014). Reviewer: Tin Yau Tam (Auburn) MSC: 15A22 15A42 15A18 PDFBibTeX XMLCite \textit{X. Liang} and \textit{R.-C. Li}, Linear Multilinear Algebra 62, No. 8, 1032--1048 (2014; Zbl 1307.15015) Full Text: DOI
Zhang, Lei-Hong; Xue, Jungong; Li, Ren-Cang Rayleigh-Ritz approximation for the linear response eigenvalue problem. (English) Zbl 1305.65126 SIAM J. Matrix Anal. Appl. 35, No. 2, 765-782 (2014). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 65F15 15A42 65L15 34L16 PDFBibTeX XMLCite \textit{L.-H. Zhang} et al., SIAM J. Matrix Anal. Appl. 35, No. 2, 765--782 (2014; Zbl 1305.65126) Full Text: DOI Link
Bai, Zhaojun; Li, Ren-Cang Minimization principles and computation for the generalized linear response eigenvalue problem. (English) Zbl 1293.65053 BIT 54, No. 1, 31-54 (2014). Reviewer: Fernando Casas (Castellon) MSC: 65F15 65L15 15A18 PDFBibTeX XMLCite \textit{Z. Bai} and \textit{R.-C. Li}, BIT 54, No. 1, 31--54 (2014; Zbl 1293.65053) Full Text: DOI
Bai, Zhaojun; Li, Ren-Cang Minimization principles for the linear response eigenvalue problem. II: Computation. (English) Zbl 1311.65102 SIAM J. Matrix Anal. Appl. 34, No. 2, 392-416 (2013). MSC: 65L15 15A18 81Q15 PDFBibTeX XMLCite \textit{Z. Bai} and \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 34, No. 2, 392--416 (2013; Zbl 1311.65102) Full Text: DOI Link
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang Deflating irreducible singular \(M\)-matrix Algebraic Riccati Equations. (English) Zbl 1271.15005 Numer. Algebra Control Optim. 3, No. 3, 491-518 (2013). MSC: 15A24 65F30 65H10 PDFBibTeX XMLCite \textit{W.-G. Wang} et al., Numer. Algebra Control Optim. 3, No. 3, 491--518 (2013; Zbl 1271.15005) Full Text: DOI
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang Erratum: Perturbation of partitioned Hermitian definite generalized eigenvalue problems. (English) Zbl 1270.15011 SIAM J. Matrix Anal. Appl. 34, No. 1, 280-281 (2013). MSC: 15A42 15A22 65F15 PDFBibTeX XMLCite \textit{R.-C. Li} et al., SIAM J. Matrix Anal. Appl. 34, No. 1, 280--281 (2013; Zbl 1270.15011) Full Text: DOI
Liang, Xin; Li, Ren-Cang; Bai, Zhaojun Trace minimization principles for positive semi-definite pencils. (English) Zbl 1262.15010 Linear Algebra Appl. 438, No. 7, 3085-3106 (2013). Reviewer: Ioannis Dassios (Thrakomakedones) MSC: 15A22 15B57 15A15 15A18 15B48 PDFBibTeX XMLCite \textit{X. Liang} et al., Linear Algebra Appl. 438, No. 7, 3085--3106 (2013; Zbl 1262.15010) Full Text: DOI
Bhatia, Rajendra; Li, Ren-Cang An interpolating family of means. (English) Zbl 1331.26053 Commun. Stoch. Anal. 6, No. 1, 15-31 (2012). MSC: 26E60 26D15 15B48 42A82 47A30 PDFBibTeX XMLCite \textit{R. Bhatia} and \textit{R.-C. Li}, Commun. Stoch. Anal. 6, No. 1, 15--31 (2012; Zbl 1331.26053)
Bai, Zhaojun; Li, Ren-Cang Minimization principles for the linear response eigenvalue problem I: Theory. (English) Zbl 1263.65078 SIAM J. Matrix Anal. Appl. 33, No. 4, 1075-1100 (2012). MSC: 65L15 15A18 81Q15 PDFBibTeX XMLCite \textit{Z. Bai} and \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 33, No. 4, 1075--1100 (2012; Zbl 1263.65078) Full Text: DOI Link
Wang, Wei-Guo; Wang, Wei-Chao; Li, Ren-Cang Alternating-directional doubling algorithm for \(M\)-matrix algebraic Riccati equations. (English) Zbl 1258.65045 SIAM J. Matrix Anal. Appl. 33, No. 1, 170-194 (2012). Reviewer: Michael Jung (Dresden) MSC: 65F30 65H10 15A24 PDFBibTeX XMLCite \textit{W.-G. Wang} et al., SIAM J. Matrix Anal. Appl. 33, No. 1, 170--194 (2012; Zbl 1258.65045) Full Text: DOI
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Wang, Wei-Guo Perturbation of multiple eigenvalues of Hermitian matrices. (English) Zbl 1242.15016 Linear Algebra Appl. 437, No. 1, 202-213 (2012). Reviewer: Ctirad Matonoha (Prague) MSC: 15A42 15B57 15A22 65F15 PDFBibTeX XMLCite \textit{R.-C. Li} et al., Linear Algebra Appl. 437, No. 1, 202--213 (2012; Zbl 1242.15016) Full Text: DOI
Xue, Jungong; Xu, Shufang; Li, Ren-Cang Accurate solutions of \(M\)-matrix algebraic Riccati equations. (English) Zbl 1260.15025 Numer. Math. 120, No. 4, 671-700 (2012). Reviewer: Martin Plešinger (Liberec) MSC: 15A24 65F30 65G99 65H10 PDFBibTeX XMLCite \textit{J. Xue} et al., Numer. Math. 120, No. 4, 671--700 (2012; Zbl 1260.15025) Full Text: DOI
Xue, Jungong; Xu, Shufang; Li, Ren-Cang Accurate solutions of \(M\)-matrix Sylvester equations. (English) Zbl 1245.65053 Numer. Math. 120, No. 4, 639-670 (2012). Reviewer: Jong Hyuk Park (Ulsan) MSC: 65F30 47A55 15A24 PDFBibTeX XMLCite \textit{J. Xue} et al., Numer. Math. 120, No. 4, 639--670 (2012; Zbl 1245.65053) Full Text: DOI
Chang, Xiao-Wen; Li, Ren-Cang Multiplicative perturbation analysis for QR factorizations. (English) Zbl 1247.65038 Numer. Algebra Control Optim. 1, No. 2, 301-316 (2011). Reviewer: Ludwig Elsner (Bielefeld) MSC: 65F05 15A23 65F35 PDFBibTeX XMLCite \textit{X.-W. Chang} and \textit{R.-C. Li}, Numer. Algebra Control Optim. 1, No. 2, 301--316 (2011; Zbl 1247.65038) Full Text: DOI
Li, Ren-Cang; Nakatsukasa, Yuji; Truhar, Ninoslav; Xu, Shufang Perturbation of partitioned Hermitian definite generalized eigenvalue problems. (English) Zbl 1230.15011 SIAM J. Matrix Anal. Appl. 32, No. 2, 642-663 (2011); erratum ibid. 34, No. 1, 280-281 (2013). Reviewer: Rodica Covaci (Cluj-Napoca) MSC: 15A42 15A22 65F15 PDFBibTeX XMLCite \textit{R.-C. Li} et al., SIAM J. Matrix Anal. Appl. 32, No. 2, 642--663 (2011; Zbl 1230.15011) Full Text: DOI Link
Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang Stable solutions of linear systems involving long chain of matrix multiplications. (English) Zbl 1220.65035 Linear Algebra Appl. 435, No. 3, 659-673 (2011). Reviewer: Constantin Popa (Constanţa) MSC: 65F05 15A12 65F35 81V80 PDFBibTeX XMLCite \textit{Z. Bai} et al., Linear Algebra Appl. 435, No. 3, 659--673 (2011; Zbl 1220.65035) Full Text: DOI
Zhou, Yunkai; Li, Ren-Cang Bounding the spectrum of large Hermitian matrices. (English) Zbl 1221.15022 Linear Algebra Appl. 435, No. 3, 480-493 (2011). Reviewer: Mihail Voicu (Iaşi) MSC: 15A18 15B57 65F15 PDFBibTeX XMLCite \textit{Y. Zhou} and \textit{R.-C. Li}, Linear Algebra Appl. 435, No. 3, 480--493 (2011; Zbl 1221.15022) Full Text: DOI
Li, Ren-Cang; Lin, Wen-Wei; Wang, Chern-Shuh Structured backward error for palindromic polynomial eigenvalue problems. (English) Zbl 1213.65063 Numer. Math. 116, No. 1, 95-122 (2010). Reviewer: Daniel Kressner (Lausanne) MSC: 65F15 15A54 PDFBibTeX XMLCite \textit{R.-C. Li} et al., Numer. Math. 116, No. 1, 95--122 (2010; Zbl 1213.65063) Full Text: DOI
Truhar, Ninoslav; Tomljanović, Zoran; Li, Ren-Cang Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts. (English) Zbl 1193.65045 Syst. Control Lett. 59, No. 3-4, 248-257 (2010). MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{N. Truhar} et al., Syst. Control Lett. 59, No. 3--4, 248--257 (2010; Zbl 1193.65045) Full Text: DOI
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav On the ADI method for Sylvester equations. (English) Zbl 1176.65050 J. Comput. Appl. Math. 233, No. 4, 1035-1045 (2009). MSC: 65F30 15A24 40C05 37L99 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Appl. Math. 233, No. 4, 1035--1045 (2009; Zbl 1176.65050) Full Text: DOI
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise Backward error of polynomial eigenproblems solved by linearization. (English) Zbl 1159.65042 SIAM J. Matrix Anal. Appl. 29, No. 4, 1218-1241 (2008). Reviewer: Alan L. Andrew (Bundoora) MSC: 65F15 15A18 65F35 15A22 15A12 PDFBibTeX XMLCite \textit{N. J. Higham} et al., SIAM J. Matrix Anal. Appl. 29, No. 4, 1218--1241 (2008; Zbl 1159.65042) Full Text: DOI Link
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang Eigenvalues of an alignment matrix in nonlinear manifold learning. (English) Zbl 1135.65019 Commun. Math. Sci. 5, No. 2, 313-329 (2007). MSC: 65F15 15A42 PDFBibTeX XMLCite \textit{C.-K. Li} et al., Commun. Math. Sci. 5, No. 2, 313--329 (2007; Zbl 1135.65019) Full Text: DOI Euclid
Ye, Qiang; Zha, Hongyuan; Li, Ren-Cang Analysis of an alignment algorithm for nonlinear dimensionality reduction. (English) Zbl 1129.62062 BIT 47, No. 4, 873-885 (2007). MSC: 62H99 62-07 15A99 62H30 65F15 15A18 PDFBibTeX XMLCite \textit{Q. Ye} et al., BIT 47, No. 4, 873--885 (2007; Zbl 1129.62062) Full Text: DOI
Li, Ren-Cang Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix. (English) Zbl 1125.15011 SIAM J. Matrix Anal. Appl. 28, No. 3, 829-844 (2006). MSC: 15A12 65F35 15A45 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 28, No. 3, 829--844 (2006; Zbl 1125.15011) Full Text: DOI Link
Li, Ren-Cang Lower bounds for the condition number of a real confluent Vandermonde matrix. (English) Zbl 1119.15008 Math. Comput. 75, No. 256, 1987-1995 (2006). MSC: 15A12 15B57 65F35 PDFBibTeX XMLCite \textit{R.-C. Li}, Math. Comput. 75, No. 256, 1987--1995 (2006; Zbl 1119.15008) Full Text: DOI
Li, Ren-Cang Relative perturbation bounds for positive polar factors of graded matrices. (English) Zbl 1099.15010 SIAM J. Matrix Anal. Appl. 27, No. 2, 424-433 (2005). Reviewer: Jaspal Singh Aujla (Jalandhar) MSC: 15A23 65F35 15A12 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 27, No. 2, 424--433 (2005; Zbl 1099.15010) Full Text: DOI
Li, Chi-Kwong; Li, Ren-Cang A note on eigenvalues of perturbed Hermitian matrices. (English) Zbl 1068.15027 Linear Algebra Appl. 395, 183-190 (2005). Reviewer: Jane M. Day (San José) MSC: 15A42 PDFBibTeX XMLCite \textit{C.-K. Li} and \textit{R.-C. Li}, Linear Algebra Appl. 395, 183--190 (2005; Zbl 1068.15027) Full Text: DOI
Truhar, Ninoslav; Li, Ren-Cang A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices. (English) Zbl 1025.15028 Linear Algebra Appl. 359, No. 1-3, 263-276 (2003). Reviewer: Váslaw Burjan (Praha) MSC: 15A42 15B57 15A18 PDFBibTeX XMLCite \textit{N. Truhar} and \textit{R.-C. Li}, Linear Algebra Appl. 359, No. 1--3, 263--276 (2003; Zbl 1025.15028) Full Text: DOI
Li, Ren-Cang On perturbations of matrix pencils with real spectra, a revisit. (English) Zbl 1047.15008 Math. Comput. 72, No. 242, 715-728 (2003). Reviewer: Aurelian Gheondea (Bucureşti) MSC: 15A22 15A42 15A21 PDFBibTeX XMLCite \textit{R.-C. Li}, Math. Comput. 72, No. 242, 715--728 (2003; Zbl 1047.15008) Full Text: DOI
Bhatia, Rajendra; Kahan, William; Li, Ren-Cang Pinchings and norms of scaled triangular matrices. (English) Zbl 1004.15020 Linear Multilinear Algebra 50, No. 1, 15-21 (2002). Reviewer: Václav Burjan (Praha) MSC: 15A42 15A60 65F35 PDFBibTeX XMLCite \textit{R. Bhatia} et al., Linear Multilinear Algebra 50, No. 1, 15--21 (2002; Zbl 1004.15020) Full Text: DOI Link
Li, Ren-Cang; Stewart, G. W. A new relative perturbation theorem for singular subspaces. (English) Zbl 0962.15012 Linear Algebra Appl. 313, No. 1-3, 41-51 (2000). Reviewer: E.Kreyszig (Ottawa) MSC: 15A42 PDFBibTeX XMLCite \textit{R.-C. Li} and \textit{G. W. Stewart}, Linear Algebra Appl. 313, No. 1--3, 41--51 (2000; Zbl 0962.15012) Full Text: DOI
Li, Ren-Cang Relative perturbation theory. IV: \(\sin 2\theta\) theorems. (English) Zbl 0963.15017 Linear Algebra Appl. 311, No. 1-3, 45-60 (2000). Reviewer: E.Kreyszig (Ottawa) MSC: 15A42 65F15 65F35 15A18 PDFBibTeX XMLCite \textit{R.-C. Li}, Linear Algebra Appl. 311, No. 1--3, 45--60 (2000; Zbl 0963.15017) Full Text: DOI
Li, Ren-Cang A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. (English) Zbl 0964.15018 SIAM J. Matrix Anal. Appl. 21, No. 2, 440-445 (1999). Reviewer: Liu Xinguo (Qingdao) MSC: 15A42 15A60 15A24 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 21, No. 2, 440--445 (1999; Zbl 0964.15018) Full Text: DOI
Li, Ren-Cang Spectral variations and Hadamard products: Some problems. (English) Zbl 0933.15032 Linear Algebra Appl. 278, No. 1-3, 317-326 (1998). MSC: 15A42 15A60 PDFBibTeX XMLCite \textit{R.-C. Li}, Linear Algebra Appl. 278, No. 1--3, 317--326 (1998; Zbl 0933.15032) Full Text: DOI
Li, Ren-Cang Relative perturbation theory. II: Eigenspace and singular subspace variations. (English) Zbl 0917.15010 SIAM J. Matrix Anal. Appl. 20, No. 2, 471-492 (1998). MSC: 15A42 65F15 65F35 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 20, No. 2, 471--492 (1998; Zbl 0917.15010) Full Text: DOI
Li, Ren-Cang Relative perturbation theory. I: Eigenvalue and singular value variations. (English) Zbl 0917.15009 SIAM J. Matrix Anal. Appl. 19, No. 4, 956-982 (1998). Reviewer: E.Kreyszig (Ottawa) MSC: 15A42 65F15 65F35 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 19, No. 4, 956--982 (1998; Zbl 0917.15009) Full Text: DOI
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang Eigenvalues of symmetrizable matrices. (English) Zbl 0898.15015 BIT 38, No. 1, 1-11 (1998). Reviewer: K.H.Kim (Montgomery) MSC: 15A42 15A12 PDFBibTeX XMLCite \textit{R. Bhatia} et al., BIT 38, No. 1, 1--11 (1998; Zbl 0898.15015) Full Text: DOI
Bhatia, Rajendra; Kittaneh, Fuad; Li, Ren-Cang Some inequalities for commutators and an application to spectral variation. II. (English) Zbl 0901.47012 Linear Multilinear Algebra 43, No. 1-3, 207-219 (1997). MSC: 47A63 47B47 15A60 PDFBibTeX XMLCite \textit{R. Bhatia} et al., Linear Multilinear Algebra 43, No. 1--3, 207--219 (1997; Zbl 0901.47012) Full Text: DOI
Li, Ren-Cang Relative perturbation theory. III: More bounds on eigenvalue variation. (English) Zbl 0917.15011 Linear Algebra Appl. 266, 337-345 (1997). Reviewer: E.Kreyszig (Ottawa) MSC: 15A42 65F15 65F35 PDFBibTeX XMLCite \textit{R.-C. Li}, Linear Algebra Appl. 266, 337--345 (1997; Zbl 0917.15011) Full Text: DOI
Li, Ren-Cang Relative perturbation bounds for the unitary polar factor. (English) Zbl 0871.15018 BIT 37, No. 1, 67-75 (1997). Reviewer: H.Havlicek (Wien) MSC: 15A45 15A23 PDFBibTeX XMLCite \textit{R.-C. Li}, BIT 37, No. 1, 67--75 (1997; Zbl 0871.15018) Full Text: DOI
Cao, Zhihao; Xie, Jinjun; Li, Ren-Cang A sharp version of Kahan’s theorem on clustered eigenvalues. (English) Zbl 0860.15017 Linear Algebra Appl. 245, 147-155 (1996). Reviewer: R.von Randow (Bonn) MSC: 15A42 15B57 PDFBibTeX XMLCite \textit{Z. Cao} et al., Linear Algebra Appl. 245, 147--155 (1996; Zbl 0860.15017) Full Text: DOI
Bhatia, Rajendra; Li, Ren-Cang On perturbations of matrix pencils with real spectra. II. (English) Zbl 0852.15008 Math. Comput. 65, No. 214, 637-645 (1996). Reviewer: H.Hollatz (Magdeburg) MSC: 15A22 15A42 65F15 PDFBibTeX XMLCite \textit{R. Bhatia} and \textit{R.-C. Li}, Math. Comput. 65, No. 214, 637--645 (1996; Zbl 0852.15008) Full Text: DOI
Li, Ren-Cang New perturbation bounds for the unitary polar factor. (English) Zbl 0817.15012 SIAM J. Matrix Anal. Appl. 16, No. 1, 327-332 (1995). Reviewer: R.von Randow (Bonn) MSC: 15A45 15A12 15A23 15A60 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 16, No. 1, 327--332 (1995; Zbl 0817.15012) Full Text: DOI
Li, Ren-Cang On eigenvalue variations of Rayleigh quotient matrix pencils of a definite pencil. (English) Zbl 0808.15005 Linear Algebra Appl. 208-209, 471-483 (1994). Reviewer: S.Sridhar (Madras) MSC: 15A18 15A42 15A22 PDFBibTeX XMLCite \textit{R.-C. Li}, Linear Algebra Appl. 208--209, 471--483 (1994; Zbl 0808.15005) Full Text: DOI
Li, Ren-Cang On perturbations of matrix pencils with real spectra. (English) Zbl 0795.15012 Math. Comput. 62, No. 205, 231-265 (1994). Reviewer: H.Hollatz (Magdeburg) MSC: 15A42 15A22 65F15 PDFBibTeX XMLCite \textit{R.-C. Li}, Math. Comput. 62, No. 205, 231--265 (1994; Zbl 0795.15012) Full Text: DOI
Li, Ren-Cang A perturbation bound for the generalized polar decomposition. (English) Zbl 0785.15007 BIT 33, No. 2, 304-308 (1993). Reviewer: Y.Kuo (Knoxville) MSC: 15A45 15A23 PDFBibTeX XMLCite \textit{R.-C. Li}, BIT 33, No. 2, 304--308 (1993; Zbl 0785.15007) Full Text: DOI
Li, Rencang Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils. (English) Zbl 0770.15009 Linear Algebra Appl. 182, 199-234 (1993). Reviewer: Li Shaokuan (Shanghai) MSC: 15A60 15A45 15A42 15A22 PDFBibTeX XMLCite \textit{R. Li}, Linear Algebra Appl. 182, 199--234 (1993; Zbl 0770.15009) Full Text: DOI
Li, Ren-Cang Bounds on perturbations of generalized singular values and of associated subspaces. (English) Zbl 0771.15002 SIAM J. Matrix Anal. Appl. 14, No. 1, 195-234 (1993). Reviewer: G.P.A.Thijsse (Rotterdam) MSC: 15A18 15A42 15A22 15A23 PDFBibTeX XMLCite \textit{R.-C. Li}, SIAM J. Matrix Anal. Appl. 14, No. 1, 195--234 (1993; Zbl 0771.15002) Full Text: DOI
Li, Ren-Cang A perturbation bound for definite pencils. (English) Zbl 0813.15017 Linear Algebra Appl. 179, 191-202 (1993). MSC: 15A42 15A22 PDFBibTeX XMLCite \textit{R.-C. Li}, Linear Algebra Appl. 179, 191--202 (1993; Zbl 0813.15017) Full Text: DOI
Li, Rencang Solution of linear matrix equation \(AXD-BXC=S\) and perturbation of eigenspaces of a matrix pencil. (English) Zbl 0793.15010 J. Comput. Math. 10, Suppl., 93-109 (1992). MSC: 15A24 15A18 PDFBibTeX XMLCite \textit{R. Li}, J. Comput. Math. 10, 93--109 (1992; Zbl 0793.15010)
Li, Rencang On eigenvalues of a Rayleigh quotient matrix. (English) Zbl 0761.15006 Linear Algebra Appl. 169, 249-255 (1992). Reviewer: J.Abaffy (Budapest) MSC: 15A18 65F15 15B57 PDFBibTeX XMLCite \textit{R. Li}, Linear Algebra Appl. 169, 249--255 (1992; Zbl 0761.15006) Full Text: DOI
Li, Rencang On the variation of the spectra of matrix pencils. (English) Zbl 0709.15010 Linear Algebra Appl. 139, 147-164 (1990). Reviewer: J.de Graaf MSC: 15A22 15A18 15A45 PDFBibTeX XMLCite \textit{R. Li}, Linear Algebra Appl. 139, 147--164 (1990; Zbl 0709.15010) Full Text: DOI
Li, Rencang QR decomposition and nonlinear eigenvalue problems. (Chinese. English summary) Zbl 0997.65527 Math. Numer. Sin. 11, No. 4, 374-385 (1989). MSC: 65F15 15A18 15A54 PDFBibTeX XMLCite \textit{R. Li}, Math. Numer. Sin. 11, No. 4, 374--385 (1989; Zbl 0997.65527)
Li, Rencang Perturbation bounds for generalized eigenvalues. II. (Chinese. English summary) Zbl 0693.15012 Math. Numer. Sin. 11, No. 3, 239-247 (1989). Reviewer: Xu Chengxian MSC: 15A42 65F15 PDFBibTeX XMLCite \textit{R. Li}, Math. Numer. Sin. 11, No. 3, 239--247 (1989; Zbl 0693.15012)
Li, Rencang Perturbation bounds for generalized eigenvalues. I. (Chinese. English summary) Zbl 0693.15011 Math. Numer. Sin. 11, No. 2, 196-204 (1989). Reviewer: Xu Chengxian MSC: 15A42 65F15 PDFBibTeX XMLCite \textit{R. Li}, Math. Numer. Sin. 11, No. 2, 196--204 (1989; Zbl 0693.15011)
Li, Rencang A converse to the Bauer-Fike type theorem. (English) Zbl 0655.15011 Linear Algebra Appl. 109, 167-178 (1988). Reviewer: Chen Zhijie MSC: 15A22 PDFBibTeX XMLCite \textit{R. Li}, Linear Algebra Appl. 109, 167--178 (1988; Zbl 0655.15011) Full Text: DOI