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
Zhou, Siyun; Liu, Xin; Xu, Liwei Stochastic Gauss-Newton algorithms for online PCA. (English) Zbl 1520.65021 J. Sci. Comput. 96, No. 3, Paper No. 72, 34 p. (2023). MSC: 65F15 15A18 62H25 65C20 PDFBibTeX XMLCite \textit{S. Zhou} et al., J. Sci. Comput. 96, No. 3, Paper No. 72, 34 p. (2023; Zbl 1520.65021) Full Text: DOI arXiv
Kaur, Avleen; Lui, S. H. New lower bounds on the minimum singular value of a matrix. (English) Zbl 1515.15011 Linear Algebra Appl. 666, 62-95 (2023). MSC: 15A18 15A42 15A60 15B57 PDFBibTeX XMLCite \textit{A. Kaur} and \textit{S. H. Lui}, Linear Algebra Appl. 666, 62--95 (2023; Zbl 1515.15011) 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
Gao, Weiguo; Li, Yingzhou; Lu, Bichen Triangularized orthogonalization-free method for solving extreme eigenvalue problems. (English) Zbl 1507.65079 J. Sci. Comput. 93, No. 3, Paper No. 63, 28 p. (2022). MSC: 65F15 15A18 65K05 PDFBibTeX XMLCite \textit{W. Gao} et al., J. Sci. Comput. 93, No. 3, Paper No. 63, 28 p. (2022; Zbl 1507.65079) Full Text: DOI arXiv
Eisenmann, Henrik; Nakatsukasa, Yuji Solving two-parameter eigenvalue problems using an alternating method. (English) Zbl 1490.65059 Linear Algebra Appl. 643, 137-160 (2022). MSC: 65F15 15A18 15A69 PDFBibTeX XMLCite \textit{H. Eisenmann} and \textit{Y. Nakatsukasa}, Linear Algebra Appl. 643, 137--160 (2022; Zbl 1490.65059) Full Text: DOI arXiv
Carson, Erin; Lund, Kathryn; Rozložník, Miroslav; Thomas, Stephen Block Gram-Schmidt algorithms and their stability properties. (English) Zbl 1490.65074 Linear Algebra Appl. 638, 150-195 (2022). MSC: 65F25 15A23 65F10 PDFBibTeX XMLCite \textit{E. Carson} et al., Linear Algebra Appl. 638, 150--195 (2022; Zbl 1490.65074) Full Text: DOI arXiv
Nigam, Nilima; Pollock, Sara A simple extrapolation method for clustered eigenvalues. (English) Zbl 1480.65085 Numer. Algorithms 89, No. 1, 115-143 (2022). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{N. Nigam} and \textit{S. Pollock}, Numer. Algorithms 89, No. 1, 115--143 (2022; Zbl 1480.65085) Full Text: DOI arXiv
Boffi, Daniele; Lu, Zhongjie; Pavarino, Luca F. Iterative ILU preconditioners for linear systems and eigenproblems. (English) Zbl 1499.65102 J. Comput. Math. 39, No. 4, 633-654 (2021). MSC: 65F08 65F15 15A23 PDFBibTeX XMLCite \textit{D. Boffi} et al., J. Comput. Math. 39, No. 4, 633--654 (2021; Zbl 1499.65102) Full Text: DOI Link
Krumnow, Christian; Pfeffer, Max; Uschmajew, André Computing eigenspaces with low rank constraints. (English) Zbl 1462.65039 SIAM J. Sci. Comput. 43, No. 1, A586-A608 (2021). MSC: 65F15 65K10 53B21 15A18 15A69 PDFBibTeX XMLCite \textit{C. Krumnow} et al., SIAM J. Sci. Comput. 43, No. 1, A586--A608 (2021; Zbl 1462.65039) Full Text: DOI
Lu, Ding Nonlinear eigenvector methods for convex minimization over the numerical range. (English) Zbl 1461.65048 SIAM J. Matrix Anal. Appl. 41, No. 4, 1771-1796 (2020). MSC: 65F15 15A60 PDFBibTeX XMLCite \textit{D. Lu}, SIAM J. Matrix Anal. Appl. 41, No. 4, 1771--1796 (2020; Zbl 1461.65048) Full Text: DOI
Nakatsukasa, Yuji Sharp error bounds for Ritz vectors and approximate singular vectors. (English) Zbl 1441.65038 Math. Comput. 89, No. 324, 1843-1866 (2020). Reviewer: Jorma K. Merikoski (Tampere) MSC: 65F15 15A18 15A42 PDFBibTeX XMLCite \textit{Y. Nakatsukasa}, Math. Comput. 89, No. 324, 1843--1866 (2020; Zbl 1441.65038) Full Text: DOI arXiv
Goldenberg, Steven; Stathopoulos, Andreas; Romero, Eloy A Golub-Kahan Davidson method for accurately computing a few singular triplets of large sparse matrices. (English) Zbl 1420.65047 SIAM J. Sci. Comput. 41, No. 4, A2172-A2192 (2019). MSC: 65F15 15A04 PDFBibTeX XMLCite \textit{S. Goldenberg} et al., SIAM J. Sci. Comput. 41, No. 4, A2172--A2192 (2019; Zbl 1420.65047) Full Text: DOI
Wu, Lingfei; Xue, Fei; Stathopoulos, Andreas TRPL+K: thick-restart preconditioned Lanczos+K method for large symmetric eigenvalue problems. (English) Zbl 1431.65047 SIAM J. Sci. Comput. 41, No. 2, A1013-A1040 (2019). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{L. Wu} et al., SIAM J. Sci. Comput. 41, No. 2, A1013--A1040 (2019; Zbl 1431.65047) Full Text: DOI arXiv
Xue, Fei A block preconditioned harmonic projection method for large-scale nonlinear eigenvalue problems. (English) Zbl 1391.65092 SIAM J. Sci. Comput. 40, No. 3, A1809-A1835 (2018). MSC: 65F15 65F50 15A18 15A22 PDFBibTeX XMLCite \textit{F. Xue}, SIAM J. Sci. Comput. 40, No. 3, A1809--A1835 (2018; Zbl 1391.65092) Full Text: DOI
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N. Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. (English) Zbl 1376.65045 J. Comput. Phys. 334, 221-239 (2017). MSC: 65F15 65F30 15A69 35Q35 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Phys. 334, 221--239 (2017; Zbl 1376.65045) Full Text: DOI arXiv
Miao, Cun-Qiang A filtered-Davidson method for large symmetric eigenvalue problems. (English) Zbl 1373.15018 East Asian J. Appl. Math. 7, No. 1, 21-37 (2017). MSC: 15A18 65F15 65F50 34L15 65N25 PDFBibTeX XMLCite \textit{C.-Q. Miao}, East Asian J. Appl. Math. 7, No. 1, 21--37 (2017; Zbl 1373.15018) Full Text: DOI
Lin, Lin Randomized estimation of spectral densities of large matrices made accurate. (English) Zbl 1364.15007 Numer. Math. 136, No. 1, 183-213 (2017). Reviewer: Constantin Popa (Constanţa) MSC: 15A18 65F15 PDFBibTeX XMLCite \textit{L. Lin}, Numer. Math. 136, No. 1, 183--213 (2017; Zbl 1364.15007) Full Text: DOI arXiv
Zhu, Peizhen; Knyazev, Andrew V. Rayleigh-Ritz majorization error bounds of mixed type. (English) Zbl 1355.15002 SIAM J. Matrix Anal. Appl. 38, No. 1, 30-49 (2017). MSC: 15A03 15A18 15A42 15B57 PDFBibTeX XMLCite \textit{P. Zhu} and \textit{A. V. Knyazev}, SIAM J. Matrix Anal. Appl. 38, No. 1, 30--49 (2017; Zbl 1355.15002) Full Text: DOI arXiv
Wen, Zaiwen; Yang, Chao; Liu, Xin; Zhang, Yin Trace-penalty minimization for large-scale eigenspace computation. (English) Zbl 1373.65026 J. Sci. Comput. 66, No. 3, 1175-1203 (2016). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F15 65K05 90C06 15A22 65Y20 PDFBibTeX XMLCite \textit{Z. Wen} et al., J. Sci. Comput. 66, No. 3, 1175--1203 (2016; Zbl 1373.65026) Full Text: DOI Link
Sirković, Petar; Kressner, Daniel Subspace acceleration for large-scale parameter-dependent Hermitian eigenproblems. (English) Zbl 1382.65104 SIAM J. Matrix Anal. Appl. 37, No. 2, 695-718 (2016). MSC: 65F15 15B57 15A18 47A55 PDFBibTeX XMLCite \textit{P. Sirković} and \textit{D. Kressner}, SIAM J. Matrix Anal. Appl. 37, No. 2, 695--718 (2016; Zbl 1382.65104) Full Text: DOI arXiv
Vecharynski, Eugene A generalization of Saad’s bound on harmonic Ritz vectors of Hermitian matrices. (English) Zbl 1382.65106 Linear Algebra Appl. 494, 219-235 (2016). MSC: 65F15 15B57 PDFBibTeX XMLCite \textit{E. Vecharynski}, Linear Algebra Appl. 494, 219--235 (2016; Zbl 1382.65106) Full Text: DOI arXiv
Vecharynski, Eugene; Yang, Chao; Pask, John E. A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix. (English) Zbl 1349.65133 J. Comput. Phys. 290, 73-89 (2015). MSC: 65F15 65F08 15B57 PDFBibTeX XMLCite \textit{E. Vecharynski} et al., J. Comput. Phys. 290, 73--89 (2015; Zbl 1349.65133) Full Text: DOI arXiv
Vecharynski, Eugene; Knyazev, Andrew Preconditioned locally harmonic residual method for computing interior eigenpairs of certain classes of Hermitian matrices. (English) Zbl 1325.65054 SIAM J. Sci. Comput. 37, No. 5, S3-S29 (2015). MSC: 65F15 65F08 65M55 15B57 PDFBibTeX XMLCite \textit{E. Vecharynski} and \textit{A. Knyazev}, SIAM J. Sci. Comput. 37, No. 5, S3--S29 (2015; Zbl 1325.65054) Full Text: DOI arXiv
Aishima, Kensuke Global convergence of the restarted Lanczos and Jacobi-Davidson methods for symmetric eigenvalue problems. (English) Zbl 1325.65050 Numer. Math. 131, No. 3, 405-423 (2015). Reviewer: Anton Iliev (Plovdiv) MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{K. Aishima}, Numer. Math. 131, No. 3, 405--423 (2015; Zbl 1325.65050) Full Text: DOI
Liu, Xin; Wen, Zaiwen; Zhang, Yin An efficient Gauss-Newton algorithm for symmetric low-rank product matrix approximations. (English) Zbl 1321.65060 SIAM J. Optim. 25, No. 3, 1571-1608 (2015). MSC: 65F20 15A83 65F10 62H35 PDFBibTeX XMLCite \textit{X. Liu} et al., SIAM J. Optim. 25, No. 3, 1571--1608 (2015; Zbl 1321.65060) Full Text: DOI
Ulbrich, Michael; Wen, Zaiwen; Yang, Chao; Klöckner, Dennis; Lu, Zhaosong A proximal gradient method for ensemble density functional theory. (English) Zbl 1325.65095 SIAM J. Sci. Comput. 37, No. 4, A1975-A2002 (2015). MSC: 65K10 15A18 65F15 90C26 90C30 PDFBibTeX XMLCite \textit{M. Ulbrich} et al., SIAM J. Sci. Comput. 37, No. 4, A1975--A2002 (2015; Zbl 1325.65095) Full Text: DOI
Lee, Namgil; Cichocki, Andrzej Estimating a few extreme singular values and vectors for large-scale matrices in tensor train format. (English) Zbl 1319.65029 SIAM J. Matrix Anal. Appl. 36, No. 3, 994-1014 (2015). MSC: 65F20 15A18 65Y20 65F50 15B05 15B52 PDFBibTeX XMLCite \textit{N. Lee} and \textit{A. Cichocki}, SIAM J. Matrix Anal. Appl. 36, No. 3, 994--1014 (2015; Zbl 1319.65029) Full Text: DOI arXiv
Abdel-Rehim, A. M.; Stathopoulos, Andreas; Orginos, Kostas Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides. (English) Zbl 1340.65056 Numer. Linear Algebra Appl. 21, No. 4, 473-493 (2014). Reviewer: Ronald B. Morgan (Waco) MSC: 65F15 65F10 15A06 15A18 65F50 81V05 PDFBibTeX XMLCite \textit{A. M. Abdel-Rehim} et al., Numer. Linear Algebra Appl. 21, No. 4, 473--493 (2014; Zbl 1340.65056) Full Text: DOI arXiv
Kressner, Daniel; Pandur, Marija Miloloža; Shao, Meiyue An indefinite variant of LOBPCG for definite matrix pencils. (English) Zbl 1297.65040 Numer. Algorithms 66, No. 4, 681-703 (2014). MSC: 65F15 65F08 15A22 PDFBibTeX XMLCite \textit{D. Kressner} et al., Numer. Algorithms 66, No. 4, 681--703 (2014; Zbl 1297.65040) Full Text: DOI Link
Nakatsukasa, Yuji The tan \(\theta \) theorem with relaxed conditions. (English) Zbl 1244.15013 Linear Algebra Appl. 436, No. 5, 1528-1534 (2012). Reviewer: Fozi Dannan (Damascus) MSC: 15A42 PDFBibTeX XMLCite \textit{Y. Nakatsukasa}, Linear Algebra Appl. 436, No. 5, 1528--1534 (2012; Zbl 1244.15013) Full Text: DOI
Zhou, Yunkai A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems. (English) Zbl 1203.65077 J. Comput. Phys. 229, No. 24, 9188-9200 (2010). MSC: 65F15 15B57 PDFBibTeX XMLCite \textit{Y. Zhou}, J. Comput. Phys. 229, No. 24, 9188--9200 (2010; Zbl 1203.65077) Full Text: DOI
Nakatsukasa, Yuji Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems. (English) Zbl 1189.15025 BIT 50, No. 1, 109-121 (2010). Reviewer: C. M. da Fonseca (Coimbra) MSC: 15A42 15A22 65F15 15B57 PDFBibTeX XMLCite \textit{Y. Nakatsukasa}, BIT 50, No. 1, 109--121 (2010; Zbl 1189.15025) Full Text: DOI