Miao, Cun-Qiang Computing eigenpairs of Hermitian matrices in augmented Krylov subspace produced by Rayleigh quotient iterations. (English) Zbl 1434.65024 J. Comput. Appl. Math. 375, Article ID 112822, 14 p. (2020). MSC: 65F08 65F15 65B05 PDFBibTeX XMLCite \textit{C.-Q. Miao}, J. Comput. Appl. Math. 375, Article ID 112822, 14 p. (2020; Zbl 1434.65024) Full Text: DOI
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
Ju, S. H.; Hsu, H. H. An out-of-core eigen-solver with OpenMP parallel scheme for large spare damped system. (English) Zbl 1480.65082 Int. J. Comput. Methods 16, No. 7, Article ID 1950038, 13 p. (2019). MSC: 65F15 65Y05 PDFBibTeX XMLCite \textit{S. H. Ju} and \textit{H. H. Hsu}, Int. J. Comput. Methods 16, No. 7, Article ID 1950038, 13 p. (2019; Zbl 1480.65082) Full Text: DOI
Izsák, Ferenc; Szekeres, Béla J. Efficient computation of matrix power-vector products: application for space-fractional diffusion problems. (English) Zbl 1432.15004 Appl. Math. Lett. 86, 70-76 (2018). Reviewer: Martin Plešinger (Liberec) MSC: 15A16 65F60 65F50 PDFBibTeX XMLCite \textit{F. Izsák} and \textit{B. J. Szekeres}, Appl. Math. Lett. 86, 70--76 (2018; Zbl 1432.15004) Full Text: DOI Link
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
Rakhuba, M. V.; Oseledets, I. V. Jacobi-Davidson method on low-rank matrix manifolds. (English) Zbl 1386.65113 SIAM J. Sci. Comput. 40, No. 2, A1149-A1170 (2018). MSC: 65F15 15A18 15A69 53B21 PDFBibTeX XMLCite \textit{M. V. Rakhuba} and \textit{I. V. Oseledets}, SIAM J. Sci. Comput. 40, No. 2, A1149--A1170 (2018; Zbl 1386.65113) Full Text: DOI arXiv
Bergamaschi, Luca; Bozzo, Enrico Computing the smallest eigenpairs of the graph Laplacian. (English) Zbl 1392.65087 S\(\vec{\text{e}}\)MA J. 75, No. 1, 1-16 (2018). MSC: 65F15 65Y20 05C82 PDFBibTeX XMLCite \textit{L. Bergamaschi} and \textit{E. Bozzo}, S\(\vec{\text{e}}\)MA J. 75, No. 1, 1--16 (2018; Zbl 1392.65087) Full Text: DOI arXiv
Bai, Zhong-Zhi; Miao, Cun-Qiang On local quadratic convergence of inexact simplified Jacobi-Davidson method. (English) Zbl 1359.65055 Linear Algebra Appl. 520, 215-241 (2017). MSC: 65F15 15B57 PDFBibTeX XMLCite \textit{Z.-Z. Bai} and \textit{C.-Q. Miao}, Linear Algebra Appl. 520, 215--241 (2017; Zbl 1359.65055) Full Text: DOI
Zhou, Yunkai; Wang, Zheng; Zhou, Aihui Accelerating large partial EVD/SVD calculations by filtered block Davidson methods. (English) Zbl 1353.65029 Sci. China, Math. 59, No. 8, 1635-1662 (2016). MSC: 65F15 65F20 65F50 PDFBibTeX XMLCite \textit{Y. Zhou} et al., Sci. China, Math. 59, No. 8, 1635--1662 (2016; Zbl 1353.65029) Full Text: DOI
Martínez, Ángeles Tuned preconditioners for the eigensolution of large SPD matrices arising in engineering problems. (English) Zbl 1413.65101 Numer. Linear Algebra Appl. 23, No. 3, 427-443 (2016). MSC: 65F15 65F08 PDFBibTeX XMLCite \textit{Á. Martínez}, Numer. Linear Algebra Appl. 23, No. 3, 427--443 (2016; Zbl 1413.65101) Full Text: DOI
Liang, Qiao; Ye, Qiang Deflation by restriction for the inverse-free preconditioned Krylov subspace method. (English) Zbl 1333.65040 Numer. Algebra Control Optim. 6, No. 1, 55-71 (2016). MSC: 65F15 65F08 PDFBibTeX XMLCite \textit{Q. Liang} and \textit{Q. Ye}, Numer. Algebra Control Optim. 6, No. 1, 55--71 (2016; Zbl 1333.65040) Full Text: DOI
Porcelli, Margherita; Binante, Vincenzo; Girardi, Maria; Padovani, Cristina; Pasquinelli, Giuseppe A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA. (English) Zbl 1320.74107 Calcolo 52, No. 2, 167-186 (2015). MSC: 74S05 65F15 65N25 65N30 70J10 PDFBibTeX XMLCite \textit{M. Porcelli} et al., Calcolo 52, No. 2, 167--186 (2015; Zbl 1320.74107) Full Text: DOI
Jia, Zhongxiao; Lin, Wen-Wei; Liu, Ching-Sung A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible \(M\)-matrix. (English) Zbl 1320.65055 Numer. Math. 130, No. 4, 645-679 (2015). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 65F50 15B48 PDFBibTeX XMLCite \textit{Z. Jia} et al., Numer. Math. 130, No. 4, 645--679 (2015; Zbl 1320.65055) Full Text: DOI arXiv
Jia, Zhongxiao; Li, Cen Inner iterations in the shift-invert residual Arnoldi method and the Jacobi-Davidson method. (English) Zbl 1312.65054 Sci. China, Math. 57, No. 8, 1733-1752 (2014). Reviewer: Michael Jung (Dresden) MSC: 65F15 65F10 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{C. Li}, Sci. China, Math. 57, No. 8, 1733--1752 (2014; Zbl 1312.65054) Full Text: DOI arXiv
Jia, ZhongXiao On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems. (English) Zbl 1292.65038 Sci. China, Math. 56, No. 10, 2145-2160 (2013). MSC: 65F15 65F10 15A18 PDFBibTeX XMLCite \textit{Z. Jia}, Sci. China, Math. 56, No. 10, 2145--2160 (2013; Zbl 1292.65038) Full Text: DOI arXiv
Liu, Xin; Hao, Chunlin; Cheng, Minghou A sequential subspace projection method for linear symmetric eigenvalue problem. (English) Zbl 1282.65044 Asia-Pac. J. Oper. Res. 30, No. 3, Article ID 1340003, 17 p. (2013). Reviewer: Alan L. Andrew (Bundoora) MSC: 65F15 PDFBibTeX XMLCite \textit{X. Liu} et al., Asia-Pac. J. Oper. Res. 30, No. 3, Article ID 1340003, 17 p. (2013; Zbl 1282.65044) Full Text: DOI
Ferronato, Massimiliano; Janna, Carlo; Pini, Giorgio Efficient parallel solution to large-size sparse eigenproblems with block FSAI preconditioning. (English) Zbl 1274.65106 Numer. Linear Algebra Appl. 19, No. 5, 797-815 (2012). Reviewer: Luca Bergamaschi (Padua) MSC: 65F15 65F50 65F08 65Y05 PDFBibTeX XMLCite \textit{M. Ferronato} et al., Numer. Linear Algebra Appl. 19, No. 5, 797--815 (2012; Zbl 1274.65106) Full Text: DOI
Jia, Zhongxiao On convergence of the inexact Rayleigh quotient iteration with MINRES. (English) Zbl 1254.65048 J. Comput. Appl. Math. 236, No. 17, 4276-4295 (2012). Reviewer: Raffaella Pavani (Milano) MSC: 65F15 65F10 PDFBibTeX XMLCite \textit{Z. Jia}, J. Comput. Appl. Math. 236, No. 17, 4276--4295 (2012; Zbl 1254.65048) Full Text: DOI arXiv
Quillen, Patrick; Ye, Qiang A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. (English) Zbl 1186.65044 J. Comput. Appl. Math. 233, No. 5, 1298-1313 (2010). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F15 65F08 PDFBibTeX XMLCite \textit{P. Quillen} and \textit{Q. Ye}, J. Comput. Appl. Math. 233, No. 5, 1298--1313 (2010; Zbl 1186.65044) Full Text: DOI
Hochstenbach, Michiel E.; Notay, Yvan Controlling inner iterations in the Jacobi-Davidson method. (English) Zbl 1191.65032 SIAM J. Matrix Anal. Appl. 31, No. 2, 460-477 (2009). Reviewer: Jinhai Chen (Hongkong) MSC: 65F15 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{Y. Notay}, SIAM J. Matrix Anal. Appl. 31, No. 2, 460--477 (2009; Zbl 1191.65032) Full Text: DOI
Robbé, Mickaël; Sadkane, Miloud; Spence, Alastair Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems. (English) Zbl 1269.65036 SIAM J. Matrix Anal. Appl. 31, No. 1, 92-113 (2009). MSC: 65F15 65F10 65F08 65F50 PDFBibTeX XMLCite \textit{M. Robbé} et al., SIAM J. Matrix Anal. Appl. 31, No. 1, 92--113 (2009; Zbl 1269.65036) Full Text: DOI Link
Jia, ZhongXiao; Wang, Zhen A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem. (English) Zbl 1179.65039 Sci. China, Ser. A 51, No. 12, 2205-2216 (2008). MSC: 65F15 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{Z. Wang}, Sci. China, Ser. A 51, No. 12, 2205--2216 (2008; Zbl 1179.65039) Full Text: DOI
Bollhöfer, Matthias; Notay, Yvan JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices. (English) Zbl 1196.65072 Comput. Phys. Commun. 177, No. 12, 951-964 (2007). MSC: 65F15 65F50 65Y15 PDFBibTeX XMLCite \textit{M. Bollhöfer} and \textit{Y. Notay}, Comput. Phys. Commun. 177, No. 12, 951--964 (2007; Zbl 1196.65072) Full Text: DOI
Freitag, Melina A.; Spence, Alastair Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem. (English) Zbl 1171.65025 ETNA, Electron. Trans. Numer. Anal. 28(2007-2008), 40-64 (2007). MSC: 65F15 15A18 65F50 PDFBibTeX XMLCite \textit{M. A. Freitag} and \textit{A. Spence}, ETNA, Electron. Trans. Numer. Anal. 28, 40--64 (2007; Zbl 1171.65025) Full Text: EuDML EMIS
Zhou, Yunkai; Saad, Yousef A Chebyshev-Davidson algorithm for large symmetric eigenproblems. (English) Zbl 1151.65321 SIAM J. Matrix Anal. Appl. 29, No. 3, 954-971 (2007). MSC: 65F15 15A18 15A23 15A90 65F25 65F50 PDFBibTeX XMLCite \textit{Y. Zhou} and \textit{Y. Saad}, SIAM J. Matrix Anal. Appl. 29, No. 3, 954--971 (2007; Zbl 1151.65321) Full Text: DOI
Voss, Heinrich A new justification of the Jacobi-Davidson method for large eigenproblems. (English) Zbl 1120.65048 Linear Algebra Appl. 424, No. 2-3, 448-455 (2007). Reviewer: R. Militaru (Craiova) MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{H. Voss}, Linear Algebra Appl. 424, No. 2--3, 448--455 (2007; Zbl 1120.65048) Full Text: DOI
Hochstenbach, M. E.; Notay, Y. The Jacobi-Davidson method. (English) Zbl 1177.65055 GAMM-Mitt. 29, No. 2, 368-382 (2006). MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{Y. Notay}, GAMM-Mitt. 29, No. 2, 368--382 (2006; Zbl 1177.65055) Full Text: DOI
Baker, C. G.; Absil, P.-A.; Gallivan, K. A. An implicit Riemannian trust-region method for the symmetric generalized eigenproblem. (English) Zbl 1155.65325 Alexandrov, Vassil N. (ed.) et al., Computational science – ICCS 2006. 6th international conference, Reading, UK, May 28–31, 2006. Proceedings, Part I. Berlin: Springer (ISBN 3-540-34379-2/pbk). Lecture Notes in Computer Science 3991, 210-217 (2006). MSC: 65F15 PDFBibTeX XMLCite \textit{C. G. Baker} et al., Lect. Notes Comput. Sci. 3991, 210--217 (2006; Zbl 1155.65325) Full Text: DOI
Pini, Giorgio; Gambolati, Giuseppe 3-D nested eigenanalysis on finite element grids. (English) Zbl 1105.65324 Commun. Numer. Methods Eng. 22, No. 7, 711-726 (2006). MSC: 65F15 PDFBibTeX XMLCite \textit{G. Pini} and \textit{G. Gambolati}, Commun. Numer. Methods Eng. 22, No. 7, 711--726 (2006; Zbl 1105.65324) Full Text: DOI
Bergamaschi, Luca; Martínez, Ángeles; Pini, Giorgio Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems. (English) Zbl 1093.65036 Appl. Math. Comput. 175, No. 2, 1694-1715 (2006). MSC: 65F15 65F50 65F35 PDFBibTeX XMLCite \textit{L. Bergamaschi} et al., Appl. Math. Comput. 175, No. 2, 1694--1715 (2006; Zbl 1093.65036) Full Text: DOI
Ovtchinnikov, E. Cluster robustness of preconditioned gradient subspace iteration eigensolvers. (English) Zbl 1101.65038 Linear Algebra Appl. 415, No. 1, 140-166 (2006). Reviewer: Daniel Kressner (Zagreb) MSC: 65F15 65F35 PDFBibTeX XMLCite \textit{E. Ovtchinnikov}, Linear Algebra Appl. 415, No. 1, 140--166 (2006; Zbl 1101.65038) Full Text: DOI
Absil, P.-A.; Baker, C. G.; Gallivan, K. A. A truncated-CG style method for symmetric generalized eigenvalue problems. (English) Zbl 1090.65042 J. Comput. Appl. Math. 189, No. 1-2, 274-285 (2006). Reviewer: Amin Boumenir (Carrollton) MSC: 65F15 PDFBibTeX XMLCite \textit{P. A. Absil} et al., J. Comput. Appl. Math. 189, No. 1--2, 274--285 (2006; Zbl 1090.65042) Full Text: DOI
Simoncini, V. Variable accuracy of matrix-vector products in projection methods for eigencomputation. (English) Zbl 1093.65037 SIAM J. Numer. Anal. 43, No. 3, 1155-1174 (2005). MSC: 65F15 PDFBibTeX XMLCite \textit{V. Simoncini}, SIAM J. Numer. Anal. 43, No. 3, 1155--1174 (2005; Zbl 1093.65037) Full Text: DOI Link
Money, James H.; Ye, Qiang Algorithm 845: EIGIFP: A MATLAB program for solving large symmetric generalized eigenvalue problems. (English) Zbl 1070.65531 ACM Trans. Math. Softw. 31, No. 2, 270-279 (2005). MSC: 65F15 15-04 65Y15 PDFBibTeX XMLCite \textit{J. H. Money} and \textit{Q. Ye}, ACM Trans. Math. Softw. 31, No. 2, 270--279 (2005; Zbl 1070.65531) Full Text: DOI
Absil, P.-A.; Sepulchre, R.; Van Dooren, P.; Mahony, R. Cubically convergent iterations for invariant subspace computation. (English) Zbl 1075.65049 SIAM J. Matrix Anal. Appl. 26, No. 1, 70-96 (2004). MSC: 65F15 PDFBibTeX XMLCite \textit{P. A. Absil} et al., SIAM J. Matrix Anal. Appl. 26, No. 1, 70--96 (2004; Zbl 1075.65049) Full Text: DOI
Notay, Y. Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem. (English) Zbl 1071.65516 Numer. Linear Algebra Appl. 9, No. 1, 21-44 (2002). MSC: 65F15 PDFBibTeX XMLCite \textit{Y. Notay}, Numer. Linear Algebra Appl. 9, No. 1, 21--44 (2002; Zbl 1071.65516) Full Text: DOI
Knyazev, Andrew V. Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. (English) Zbl 0992.65028 SIAM J. Sci. Comput. 23, No. 2, 517-541 (2001). MSC: 65F15 65F35 PDFBibTeX XMLCite \textit{A. V. Knyazev}, SIAM J. Sci. Comput. 23, No. 2, 517--541 (2001; Zbl 0992.65028) Full Text: DOI