Caruso, Noè Angelo; Michelangeli, Alessandro Krylov solvability under perturbations of abstract inverse linear problems. (English) Zbl 07709524 J. Appl. Anal. 29, No. 1, 3-29 (2023). MSC: 47N40 65J22 47B37 65J05 PDFBibTeX XMLCite \textit{N. A. Caruso} and \textit{A. Michelangeli}, J. Appl. Anal. 29, No. 1, 3--29 (2023; Zbl 07709524) Full Text: DOI arXiv
Evstigneev, N. M.; Ryabkov, O. I.; Bocharov, A. N.; Petrovskiy, V. P.; Teplyakov, I. O. Compensated summation and dot product algorithms for floating-point vectors on parallel architectures: error bounds, implementation and application in the Krylov subspace methods. (English) Zbl 1492.65374 J. Comput. Appl. Math. 414, Article ID 114434, 37 p. (2022). MSC: 65Y10 65Y05 65G50 65F08 PDFBibTeX XMLCite \textit{N. M. Evstigneev} et al., J. Comput. Appl. Math. 414, Article ID 114434, 37 p. (2022; Zbl 1492.65374) Full Text: DOI
Jawecki, Tobias A study of defect-based error estimates for the Krylov approximation of \(\varphi\)-functions. (English) Zbl 07512667 Numer. Algorithms 90, No. 1, 323-361 (2022). MSC: 65F60 65L70 65N22 PDFBibTeX XMLCite \textit{T. Jawecki}, Numer. Algorithms 90, No. 1, 323--361 (2022; Zbl 07512667) Full Text: DOI arXiv
Gu, Xian-Ming; Lei, Siu-Long; Zhang, Ke; Shen, Zhao-Li; Wen, Chun; Carpentieri, Bruno A Hessenberg-type algorithm for computing PageRank problems. (English) Zbl 1485.65037 Numer. Algorithms 89, No. 4, 1845-1863 (2022). MSC: 65F15 65F10 65Y20 PDFBibTeX XMLCite \textit{X.-M. Gu} et al., Numer. Algorithms 89, No. 4, 1845--1863 (2022; Zbl 1485.65037) Full Text: DOI arXiv
Li, Zhe; Zhang, Chunlei The verification of multiplicity support of a defective eigenvalue of a real matrix. (English) Zbl 1510.65067 Appl. Math. Comput. 414, Article ID 126671, 15 p. (2022). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{Z. Li} and \textit{C. Zhang}, Appl. Math. Comput. 414, Article ID 126671, 15 p. (2022; Zbl 1510.65067) Full Text: DOI
Pozza, Stefano; Pranić, Miroslav The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization. (English) Zbl 1486.65030 Numer. Algorithms 88, No. 2, 647-678 (2021). MSC: 65D30 65D32 PDFBibTeX XMLCite \textit{S. Pozza} and \textit{M. Pranić}, Numer. Algorithms 88, No. 2, 647--678 (2021; Zbl 1486.65030) Full Text: DOI arXiv
Miyajima, Shinya Fast verification for the Perron pair of an irreducible nonnegative matrix. (English) Zbl 07373353 Electron. J. Linear Algebra 37, 402-415 (2021). MSC: 65F15 15A18 65G20 PDFBibTeX XMLCite \textit{S. Miyajima}, Electron. J. Linear Algebra 37, 402--415 (2021; Zbl 07373353) Full Text: Link
Miyajima, Shinya Computing enclosures for the matrix Mittag-Leffler function. (English) Zbl 1470.65080 J. Sci. Comput. 87, No. 2, Paper No. 62, 22 p. (2021). MSC: 65F60 15A16 65G20 26A33 33E12 33F05 PDFBibTeX XMLCite \textit{S. Miyajima}, J. Sci. Comput. 87, No. 2, Paper No. 62, 22 p. (2021; Zbl 1470.65080) Full Text: DOI
Montoison, Alexis; Orban, Dominique BiLQ: an iterative method for nonsymmetric linear systems with a quasi-minimum error property. (English) Zbl 1458.65032 SIAM J. Matrix Anal. Appl. 41, No. 3, 1145-1166 (2020). MSC: 65F10 65F25 65F50 PDFBibTeX XMLCite \textit{A. Montoison} and \textit{D. Orban}, SIAM J. Matrix Anal. Appl. 41, No. 3, 1145--1166 (2020; Zbl 1458.65032) Full Text: DOI arXiv
Lessard, J. P.; Mireles James, J. D. A functional analytic approach to validated numerics for eigenvalues of delay equations. (English) Zbl 07235863 J. Comput. Dyn. 7, No. 1, 123-158 (2020). MSC: 65G20 37B30 34K08 34K20 65M70 PDFBibTeX XMLCite \textit{J. P. Lessard} and \textit{J. D. Mireles James}, J. Comput. Dyn. 7, No. 1, 123--158 (2020; Zbl 07235863) Full Text: DOI
Miyajima, Shinya Enclosing Moore-Penrose inverses. (English) Zbl 1436.15005 Calcolo 57, No. 1, Paper No. 7, 16 p. (2020). MSC: 15A09 65F20 PDFBibTeX XMLCite \textit{S. Miyajima}, Calcolo 57, No. 1, Paper No. 7, 16 p. (2020; Zbl 1436.15005) Full Text: DOI
Gu, Xian-Ming; Huang, Ting-Zhu; Carpentieri, Bruno; Imakura, Akira; Zhang, Ke; Du, Lei Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously. (English) Zbl 1434.65027 J. Comput. Appl. Math. 375, Article ID 112788, 16 p. (2020). MSC: 65F10 65F08 65N22 PDFBibTeX XMLCite \textit{X.-M. Gu} et al., J. Comput. Appl. Math. 375, Article ID 112788, 16 p. (2020; Zbl 1434.65027) Full Text: DOI arXiv
Jawecki, Tobias; Auzinger, Winfried; Koch, Othmar Computable upper error bounds for Krylov approximations to matrix exponentials and associated \(\varphi\)-functions. (English) Zbl 1432.65053 BIT 60, No. 1, 157-197 (2020). MSC: 65F60 15A16 65F15 PDFBibTeX XMLCite \textit{T. Jawecki} et al., BIT 60, No. 1, 157--197 (2020; Zbl 1432.65053) Full Text: DOI arXiv
Zhong, Hong-Xiu; Gu, Xian-Ming A flexible and adaptive simpler GMRES with deflated restarting for shifted linear systems. (English) Zbl 1442.65052 Comput. Math. Appl. 78, No. 3, 997-1007 (2019). MSC: 65F10 PDFBibTeX XMLCite \textit{H.-X. Zhong} and \textit{X.-M. Gu}, Comput. Math. Appl. 78, No. 3, 997--1007 (2019; Zbl 1442.65052) Full Text: DOI arXiv
Paige, Christopher C. Accuracy of the Lanczos process for the eigenproblem and solution of equations. (English) Zbl 1427.65044 SIAM J. Matrix Anal. Appl. 40, No. 4, 1371-1398 (2019). MSC: 65F10 65F15 65F25 65F50 65G50 15A18 15B57 PDFBibTeX XMLCite \textit{C. C. Paige}, SIAM J. Matrix Anal. Appl. 40, No. 4, 1371--1398 (2019; Zbl 1427.65044) Full Text: DOI
Ramezani, Z.; Toutounian, F. Extended and rational Hessenberg methods for the evaluation of matrix functions. (English) Zbl 07074125 BIT 59, No. 2, 523-545 (2019). MSC: 65F10 PDFBibTeX XMLCite \textit{Z. Ramezani} and \textit{F. Toutounian}, BIT 59, No. 2, 523--545 (2019; Zbl 07074125) Full Text: DOI
Baumann, Manuel; van Gijzen, Martin B. An efficient two-level preconditioner for multi-frequency wave propagation problems. (English) Zbl 1406.65104 Appl. Numer. Math. 135, 316-332 (2019). MSC: 65N30 65F10 65F08 74J30 35Q74 PDFBibTeX XMLCite \textit{M. Baumann} and \textit{M. B. van Gijzen}, Appl. Numer. Math. 135, 316--332 (2019; Zbl 1406.65104) Full Text: DOI
Astudillo, R.; de Gier, J. M.; van Gijzen, M. B. Accelerating the induced dimension reduction method using spectral information. (English) Zbl 1408.65011 J. Comput. Appl. Math. 345, 33-47 (2019). Reviewer: Jurjen Duintjer Tebbens (Praha) MSC: 65F10 65F50 65F15 PDFBibTeX XMLCite \textit{R. Astudillo} et al., J. Comput. Appl. Math. 345, 33--47 (2019; Zbl 1408.65011) Full Text: DOI Link
Freitag, Melina A.; Kürschner, Patrick; Pestana, Jennifer GMRES convergence bounds for eigenvalue problems. (English) Zbl 1391.65065 Comput. Methods Appl. Math. 18, No. 2, 203-222 (2018). MSC: 65F10 15A18 65F08 65F15 65N25 PDFBibTeX XMLCite \textit{M. A. Freitag} et al., Comput. Methods Appl. Math. 18, No. 2, 203--222 (2018; Zbl 1391.65065) Full Text: DOI arXiv Link
Li, Zhe; Wan, Baocheng; Gao, Ruimei Verified error bounds for eigenvalues of geometric multiplicity \(q\) and corresponding invariant subspaces. (English) Zbl 1384.65027 Numer. Algorithms 77, No. 2, 631-652 (2018). Reviewer: Anton Iliev (Plovdiv) MSC: 65F15 65G20 PDFBibTeX XMLCite \textit{Z. Li} et al., Numer. Algorithms 77, No. 2, 631--652 (2018; Zbl 1384.65027) Full Text: DOI
Gu, Xian-Ming; Huang, Ting-Zhu; Yin, Guojian; Carpentieri, Bruno; Wen, Chun; Du, Lei Restarted Hessenberg method for solving shifted nonsymmetric linear systems. (English) Zbl 1377.65042 J. Comput. Appl. Math. 331, 166-177 (2018). MSC: 65F10 65F25 35R11 65M06 PDFBibTeX XMLCite \textit{X.-M. Gu} et al., J. Comput. Appl. Math. 331, 166--177 (2018; Zbl 1377.65042) Full Text: DOI arXiv Link
Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir An iterative solver for the 3D Helmholtz equation. (English) Zbl 1378.35088 J. Comput. Phys. 345, 330-344 (2017). MSC: 35J05 65N99 35A24 35A22 PDFBibTeX XMLCite \textit{M. Belonosov} et al., J. Comput. Phys. 345, 330--344 (2017; Zbl 1378.35088) Full Text: DOI
Il’in, V. P. Iterative processes in the Krylov-Sonneveld subspaces. (English. Russian original) Zbl 1373.65020 J. Math. Sci., New York 224, No. 6, 890-899 (2017); translation from Zap. Nauchn. Semin. POMI 453, 114-130 (2016). MSC: 65F10 65F08 PDFBibTeX XMLCite \textit{V. P. Il'in}, J. Math. Sci., New York 224, No. 6, 890--899 (2017; Zbl 1373.65020); translation from Zap. Nauchn. Semin. POMI 453, 114--130 (2016) Full Text: DOI
Astudillo, R.; van Gijzen, M. B. Induced dimension reduction method to solve the quadratic eigenvalue problem. (English) Zbl 1368.65055 Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 203-211 (2017). MSC: 65F15 PDFBibTeX XMLCite \textit{R. Astudillo} and \textit{M. B. van Gijzen}, Lect. Notes Comput. Sci. 10187, 203--211 (2017; Zbl 1368.65055) Full Text: DOI
Chen, Jie; McInnes, Lois C.; Zhang, Hong Analysis and practical use of flexible biCGStab. (English) Zbl 1372.65097 J. Sci. Comput. 68, No. 2, 803-825 (2016). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 65F08 PDFBibTeX XMLCite \textit{J. Chen} et al., J. Sci. Comput. 68, No. 2, 803--825 (2016; Zbl 1372.65097) Full Text: DOI
Il’in, V. P. Problems of parallel solution of large systems of linear algebraic equations. (English. Russian original) Zbl 1347.65064 J. Math. Sci., New York 216, No. 6, 795-804 (2016); translation from Zap. Nauchn. Semin. POMI 439, 112-127 (2015). MSC: 65F10 65F08 65Y05 65Y10 65N55 PDFBibTeX XMLCite \textit{V. P. Il'in}, J. Math. Sci., New York 216, No. 6, 795--804 (2016; Zbl 1347.65064); translation from Zap. Nauchn. Semin. POMI 439, 112--127 (2015) Full Text: DOI
Astudillo, R.; van Gijzen, M. B. A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices. (English) Zbl 1342.65113 J. Comput. Appl. Math. 296, 24-35 (2016). MSC: 65F15 65F50 PDFBibTeX XMLCite \textit{R. Astudillo} and \textit{M. B. van Gijzen}, J. Comput. Appl. Math. 296, 24--35 (2016; Zbl 1342.65113) Full Text: DOI
Baumann, Manuel; van Gijzen, Martin B. Nested Krylov methods for shifted linear systems. (English) Zbl 06502306 SIAM J. Sci. Comput. 37, No. 5, S90-S112 (2015). MSC: 65F10 65F50 65F08 PDFBibTeX XMLCite \textit{M. Baumann} and \textit{M. B. van Gijzen}, SIAM J. Sci. Comput. 37, No. 5, S90--S112 (2015; Zbl 06502306) Full Text: DOI Link
van Gijzen, Martin B.; Sleijpen, Gerard L. G.; Zemke, Jens-Peter M. Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems. (English) Zbl 1363.65058 Numer. Linear Algebra Appl. 22, No. 1, 1-25 (2015). MSC: 65F10 65F50 PDFBibTeX XMLCite \textit{M. B. van Gijzen} et al., Numer. Linear Algebra Appl. 22, No. 1, 1--25 (2015; Zbl 1363.65058) Full Text: DOI Link
Carson, Erin; Demmel, James W. Accuracy of the \(s\)-step Lanczos method for the symmetric eigenproblem in finite precision. (English) Zbl 1319.65024 SIAM J. Matrix Anal. Appl. 36, No. 2, 793-819 (2015). MSC: 65F15 65G50 PDFBibTeX XMLCite \textit{E. Carson} and \textit{J. W. Demmel}, SIAM J. Matrix Anal. Appl. 36, No. 2, 793--819 (2015; Zbl 1319.65024) Full Text: DOI
Gutknecht, Martin H. Revisiting \((k,\ell)\)-step methods. (English) Zbl 1317.65119 Numer. Algorithms 69, No. 2, 455-469 (2015). MSC: 65H10 PDFBibTeX XMLCite \textit{M. H. Gutknecht}, Numer. Algorithms 69, No. 2, 455--469 (2015; Zbl 1317.65119) Full Text: DOI
Du, Lei; Sogabe, Tomohiro; Zhang, Shao-Liang IDR(\(s\)) for solving shifted nonsymmetric linear systems. (English) Zbl 1310.65037 J. Comput. Appl. Math. 274, 35-43 (2015). MSC: 65F10 PDFBibTeX XMLCite \textit{L. Du} et al., J. Comput. Appl. Math. 274, 35--43 (2015; Zbl 1310.65037) Full Text: DOI
Sun, Dong-Lin; Jing, Yan-Fei; Huang, Ting-Zhu; Carpentieri, Bruno A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems. (English) Zbl 1367.65053 Comput. Math. Appl. 67, No. 10, 1743-1755 (2014). MSC: 65F10 15A06 PDFBibTeX XMLCite \textit{D.-L. Sun} et al., Comput. Math. Appl. 67, No. 10, 1743--1755 (2014; Zbl 1367.65053) Full Text: DOI Link
Aihara, Kensuke; Abe, Kuniyoshi; Ishiwata, Emiko A quasi-minimal residual variant of IDRstab using the residual smoothing technique. (English) Zbl 1336.65035 Appl. Math. Comput. 236, 67-77 (2014). MSC: 65F10 PDFBibTeX XMLCite \textit{K. Aihara} et al., Appl. Math. Comput. 236, 67--77 (2014; Zbl 1336.65035) Full Text: DOI
Yeung, Man-Chung ML(\(n\))BiCGStabt: a ML(\(n\))BiCGStab variant with \(\mathbf A\)-transpose. (English) Zbl 1303.65017 J. Comput. Appl. Math. 272, 57-69 (2014). MSC: 65F10 65F15 65F25 65F30 PDFBibTeX XMLCite \textit{M.-C. Yeung}, J. Comput. Appl. Math. 272, 57--69 (2014; Zbl 1303.65017) Full Text: DOI arXiv
Aihara, Kensuke; Abe, Kuniyoshi; Ishiwata, Emiko A variant of IDRstab with reliable update strategies for solving sparse linear systems. (English) Zbl 1291.65093 J. Comput. Appl. Math. 259, Part A, 244-258 (2014). MSC: 65F10 65F50 PDFBibTeX XMLCite \textit{K. Aihara} et al., J. Comput. Appl. Math. 259, Part A, 244--258 (2014; Zbl 1291.65093) Full Text: DOI
Meng, Jing; Zhu, Pei-Yong; Li, Hou-Biao A block \(\mathrm{GCROT}(m, k)\) method for linear systems with multiple right-hand sides. (English) Zbl 1291.65105 J. Comput. Appl. Math. 255, 544-554 (2014). MSC: 65F10 PDFBibTeX XMLCite \textit{J. Meng} et al., J. Comput. Appl. Math. 255, 544--554 (2014; Zbl 1291.65105) Full Text: DOI
Paige, Christopher C.; Panayotov, Ivo; Zemke, Jens-Peter M. An augmented analysis of the perturbed two-sided Lanczos tridiagonalization process. (English) Zbl 1291.65130 Linear Algebra Appl. 447, 119-132 (2014). MSC: 65F15 PDFBibTeX XMLCite \textit{C. C. Paige} et al., Linear Algebra Appl. 447, 119--132 (2014; Zbl 1291.65130) Full Text: DOI
Rendel, Olaf; Rizvanolli, Anisa; Zemke, Jens-Peter M. IDR: a new generation of Krylov subspace methods? (English) Zbl 1305.65118 Linear Algebra Appl. 439, No. 4, 1040-1061 (2013). MSC: 65F10 65F15 PDFBibTeX XMLCite \textit{O. Rendel} et al., Linear Algebra Appl. 439, No. 4, 1040--1061 (2013; Zbl 1305.65118) Full Text: DOI
Abderramán Marrero, J.; Tomeo, V. On the closed representation for the inverses of Hessenberg matrices. (English) Zbl 1237.15005 J. Comput. Appl. Math. 236, No. 12, 2962-2970 (2012). MSC: 15A09 11B83 15A15 33C45 47A10 65F05 PDFBibTeX XMLCite \textit{J. Abderramán Marrero} and \textit{V. Tomeo}, J. Comput. Appl. Math. 236, No. 12, 2962--2970 (2012; Zbl 1237.15005) Full Text: DOI
Du, Lei; Sogabe, Tomohiro; Zhang, Shao-Liang A variant of the IDR\((s)\) method with the quasi-minimal residual strategy. (English) Zbl 1300.65016 J. Comput. Appl. Math. 236, No. 5, 621-630 (2011). MSC: 65F10 PDFBibTeX XMLCite \textit{L. Du} et al., J. Comput. Appl. Math. 236, No. 5, 621--630 (2011; Zbl 1300.65016) Full Text: DOI
Du, Kui GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem. (English) Zbl 1227.65032 Appl. Numer. Math. 61, No. 9, 977-988 (2011). Reviewer: R. Militaru (Craiova) MSC: 65F10 78A45 PDFBibTeX XMLCite \textit{K. Du}, Appl. Numer. Math. 61, No. 9, 977--988 (2011; Zbl 1227.65032) Full Text: DOI
Rump, Siegfried M.; Graillat, Stef Verified error bounds for multiple roots of systems of nonlinear equations. (English) Zbl 1201.65081 Numer. Algorithms 54, No. 3, 359-377 (2010). Reviewer: Svetoslav Markov (Sofia) MSC: 65H10 65G20 65H04 65F15 PDFBibTeX XMLCite \textit{S. M. Rump} and \textit{S. Graillat}, Numer. Algorithms 54, No. 3, 359--377 (2010; Zbl 1201.65081) Full Text: DOI
Galántai, A.; Hegedűs, C. J. Hyman’s method revisited. (English) Zbl 1181.65053 J. Comput. Appl. Math. 226, No. 2, 246-258 (2009). Reviewer: George A. Gravvanis (Xanthi) MSC: 65F15 15A18 15A21 PDFBibTeX XMLCite \textit{A. Galántai} and \textit{C. J. Hegedűs}, J. Comput. Appl. Math. 226, No. 2, 246--258 (2009; Zbl 1181.65053) Full Text: DOI
Zemke, Jens-Peter M. Abstract perturbed Krylov methods. (English) Zbl 1125.65029 Linear Algebra Appl. 424, No. 2-3, 405-434 (2007). Reviewer: Dietrich Braess (Bochum) MSC: 65F10 PDFBibTeX XMLCite \textit{J.-P. M. Zemke}, Linear Algebra Appl. 424, No. 2--3, 405--434 (2007; Zbl 1125.65029) Full Text: DOI Link
Kolev, Lubomir V. Outer interval solution of the eigenvalue problem under general form parametric dependencies. (English) Zbl 1085.65032 Reliab. Comput. 12, No. 2, 121-140 (2006). Reviewer: Jiří Rohn (Praha) MSC: 65F15 65G30 PDFBibTeX XMLCite \textit{L. V. Kolev}, Reliab. Comput. 12, No. 2, 121--140 (2006; Zbl 1085.65032) Full Text: DOI