Petkov, Petko H. Jordan-Schur algorithms for computing the matrix exponential. (English) Zbl 07665365 Int. J. Math. Math. Sci. 2023, Article ID 4908185, 17 p. (2023). MSC: 65Fxx 15Axx 65Dxx PDFBibTeX XMLCite \textit{P. H. Petkov}, Int. J. Math. Math. Sci. 2023, Article ID 4908185, 17 p. (2023; Zbl 07665365) Full Text: DOI
Sastre, Jorge; Ibáñez, Javier On the backward and forward error of approximations of analytic functions and applications to the computation of matrix functions. (English) Zbl 1502.65022 J. Comput. Appl. Math. 419, Article ID 114706, 18 p. (2023). MSC: 65F60 65D15 15A16 26C15 41-04 41A10 PDFBibTeX XMLCite \textit{J. Sastre} and \textit{J. Ibáñez}, J. Comput. Appl. Math. 419, Article ID 114706, 18 p. (2023; Zbl 1502.65022) Full Text: DOI
Bentbib, A. H.; Ghomari, M. El; Jbilou, K. An extended-rational Arnoldi method for large matrix exponential evaluations. (English) Zbl 1492.65117 J. Sci. Comput. 91, No. 2, Paper No. 36, 23 p. (2022). MSC: 65F60 65D15 15A16 PDFBibTeX XMLCite \textit{A. H. Bentbib} et al., J. Sci. Comput. 91, No. 2, Paper No. 36, 23 p. (2022; Zbl 1492.65117) Full Text: DOI
Gawlik, Evan S.; Nakatsukasa, Yuji Approximating the \(p\)th root by composite rational functions. (English) Zbl 1471.41006 J. Approx. Theory 266, Article ID 105577, 16 p. (2021). Reviewer: Josef Kofroň (Praha) MSC: 41A20 41A25 41A50 65D15 PDFBibTeX XMLCite \textit{E. S. Gawlik} and \textit{Y. Nakatsukasa}, J. Approx. Theory 266, Article ID 105577, 16 p. (2021; Zbl 1471.41006) Full Text: DOI arXiv
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
Gawlik, Evan S. Zolotarev iterations for the Matrix square Root. (English) Zbl 1420.65057 SIAM J. Matrix Anal. Appl. 40, No. 2, 696-719 (2019). MSC: 65F30 65F60 41A20 49K35 PDFBibTeX XMLCite \textit{E. S. Gawlik}, SIAM J. Matrix Anal. Appl. 40, No. 2, 696--719 (2019; Zbl 1420.65057) Full Text: DOI arXiv
Cardoso, João R.; Sadeghi, Amir Computation of matrix gamma function. (English) Zbl 07074116 BIT 59, No. 2, 343-370 (2019). MSC: 65F30 65F60 33B15 PDFBibTeX XMLCite \textit{J. R. Cardoso} and \textit{A. Sadeghi}, BIT 59, No. 2, 343--370 (2019; Zbl 07074116) Full Text: DOI arXiv
Musco, Cameron; Netrapalli, Praneeth; Sidford, Aaron; Ubaru, Shashanka; Woodruff, David P. Spectrum approximation beyond fast matrix multiplication: algorithms and hardness. (English) Zbl 1462.68082 Karlin, Anna R. (ed.), 9th innovations in theoretical computer science conference, ITCS 2018, Cambridge, MA, USA, January 11–14, 2018. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 94, Article 8, 21 p. (2018). MSC: 68Q25 15A18 15A60 65F15 65F35 68Q17 68R10 PDFBibTeX XMLCite \textit{C. Musco} et al., LIPIcs -- Leibniz Int. Proc. Inform. 94, Article 8, 21 p. (2018; Zbl 1462.68082) Full Text: DOI arXiv
Nadukandi, Prashanth; Higham, Nicholas J. Computing the wave-kernel matrix functions. (English) Zbl 1403.65020 SIAM J. Sci. Comput. 40, No. 6, A4060-A4082 (2018). MSC: 65F30 15A60 65F60 PDFBibTeX XMLCite \textit{P. Nadukandi} and \textit{N. J. Higham}, SIAM J. Sci. Comput. 40, No. 6, A4060--A4082 (2018; Zbl 1403.65020) Full Text: DOI
Pozza, Stefano; Pranić, Miroslav S.; Strakoš, Zdeněk The Lanczos algorithm and complex Gauss quadrature. (English) Zbl 06965964 ETNA, Electron. Trans. Numer. Anal. 50, 1-19 (2018). MSC: 65D15 65D32 65F10 47B36 PDFBibTeX XMLCite \textit{S. Pozza} et al., ETNA, Electron. Trans. Numer. Anal. 50, 1--19 (2018; Zbl 06965964) Full Text: DOI Link
Fasi, Massimiliano; Higham, Nicholas J. Multiprecision algorithms for computing the matrix logarithm. (English) Zbl 1390.15073 SIAM J. Matrix Anal. Appl. 39, No. 1, 472-491 (2018). MSC: 15A60 65F30 65F60 PDFBibTeX XMLCite \textit{M. Fasi} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 39, No. 1, 472--491 (2018; Zbl 1390.15073) Full Text: DOI
Kressner, Daniel; Luce, Robert Fast computation of the matrix exponential for a Toeplitz matrix. (English) Zbl 1386.65131 SIAM J. Matrix Anal. Appl. 39, No. 1, 23-47 (2018). MSC: 65F60 15B05 65Y20 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{R. Luce}, SIAM J. Matrix Anal. Appl. 39, No. 1, 23--47 (2018; Zbl 1386.65131) Full Text: DOI arXiv
Sastre, J. Efficient evaluation of matrix polynomials. (English) Zbl 1432.65029 Linear Algebra Appl. 539, 229-250 (2018). MSC: 65D99 15A99 65Y05 PDFBibTeX XMLCite \textit{J. Sastre}, Linear Algebra Appl. 539, 229--250 (2018; Zbl 1432.65029) Full Text: DOI Link
Benzi, Michele; Simoncini, Valeria Approximation of functions of large matrices with Kronecker structure. (English) Zbl 1365.65134 Numer. Math. 135, No. 1, 1-26 (2017). Reviewer: Frank Uhlig (Auburn) MSC: 65F60 65F50 65D15 PDFBibTeX XMLCite \textit{M. Benzi} and \textit{V. Simoncini}, Numer. Math. 135, No. 1, 1--26 (2017; Zbl 1365.65134) Full Text: DOI arXiv
Reichel, Lothar; Spalević, Miodrag M.; Tang, Tunan Generalized averaged Gauss quadrature rules for the approximation of matrix functionals. (English) Zbl 1352.65089 BIT 56, No. 3, 1045-1067 (2016). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 65D15 65F60 41A55 PDFBibTeX XMLCite \textit{L. Reichel} et al., BIT 56, No. 3, 1045--1067 (2016; Zbl 1352.65089) Full Text: DOI
Frommer, Andreas; Schweitzer, Marcel Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions. (English) Zbl 1353.65038 BIT 56, No. 3, 865-892 (2016). Reviewer: Constantin Popa (Constanţa) MSC: 65F60 65F50 65F10 65F30 65D32 PDFBibTeX XMLCite \textit{A. Frommer} and \textit{M. Schweitzer}, BIT 56, No. 3, 865--892 (2016; Zbl 1353.65038) Full Text: DOI
Aprahamian, Mary; Higham, Nicholas J. Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. (English) Zbl 1388.15012 SIAM J. Matrix Anal. Appl. 37, No. 4, 1453-1477 (2016). MSC: 15A24 65F30 65F60 PDFBibTeX XMLCite \textit{M. Aprahamian} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 37, No. 4, 1453--1477 (2016; Zbl 1388.15012) Full Text: DOI
Nakatsukasa, Yuji; Freund, Roland W. Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: the power of Zolotarev’s functions. (English) Zbl 1383.15012 SIAM Rev. 58, No. 3, 461-493 (2016). MSC: 15A23 65F15 65F30 65G50 PDFBibTeX XMLCite \textit{Y. Nakatsukasa} and \textit{R. W. Freund}, SIAM Rev. 58, No. 3, 461--493 (2016; Zbl 1383.15012) Full Text: DOI Link
Iannazzo, Bruno The geometric mean of two matrices from a computational viewpoint. (English) Zbl 1374.65083 Numer. Linear Algebra Appl. 23, No. 2, 208-229 (2016). MSC: 65F60 15B48 47A64 26E60 PDFBibTeX XMLCite \textit{B. Iannazzo}, Numer. Linear Algebra Appl. 23, No. 2, 208--229 (2016; Zbl 1374.65083) Full Text: DOI arXiv
Güttel, Stefan; Nakatsukasa, Yuji Scaled and squared subdiagonal Padé approximation for the matrix exponential. (English) Zbl 1382.65125 SIAM J. Matrix Anal. Appl. 37, No. 1, 145-170 (2016). MSC: 65F60 15A16 15A23 65F30 41A20 41A21 65G50 PDFBibTeX XMLCite \textit{S. Güttel} and \textit{Y. Nakatsukasa}, SIAM J. Matrix Anal. Appl. 37, No. 1, 145--170 (2016; Zbl 1382.65125) Full Text: DOI
Cardoso, João R.; Ziȩtak, Krystyna On a sub-Stiefel Procrustes problem arising in computer vision. (English) Zbl 1363.65031 Numer. Linear Algebra Appl. 22, No. 3, 523-547 (2015). MSC: 65D19 15B10 65F30 PDFBibTeX XMLCite \textit{J. R. Cardoso} and \textit{K. Ziȩtak}, Numer. Linear Algebra Appl. 22, No. 3, 523--547 (2015; Zbl 1363.65031) Full Text: DOI
Kolesnikov, D. A.; Oseledets, I. V. From low-rank approximation to a rational Krylov subspace method for the Lyapunov equation. (English) Zbl 1327.65064 SIAM J. Matrix Anal. Appl. 36, No. 4, 1622-1637 (2015). MSC: 65F10 65F30 15A06 93B40 PDFBibTeX XMLCite \textit{D. A. Kolesnikov} and \textit{I. V. Oseledets}, SIAM J. Matrix Anal. Appl. 36, No. 4, 1622--1637 (2015; Zbl 1327.65064) Full Text: DOI arXiv
Botchev, M. A.; Oseledets, I. V.; Tyrtyshnikov, E. E. Iterative across-time solution of linear differential equations: Krylov subspace versus waveform relaxation. (English) Zbl 1368.65107 Comput. Math. Appl. 67, No. 12, 2088-2098 (2014). MSC: 65L05 65F30 65M20 PDFBibTeX XMLCite \textit{M. A. Botchev} et al., Comput. Math. Appl. 67, No. 12, 2088--2098 (2014; Zbl 1368.65107) Full Text: DOI
Tsitouras, Ch.; Katsikis, V. N. Bounds for variable degree rational \(L_\infty\) approximations to the matrix cosine. (English) Zbl 1348.65083 Comput. Phys. Commun. 185, No. 11, 2834-2840 (2014). MSC: 65F60 65D15 41A50 15A16 PDFBibTeX XMLCite \textit{Ch. Tsitouras} and \textit{V. N. Katsikis}, Comput. Phys. Commun. 185, No. 11, 2834--2840 (2014; Zbl 1348.65083) Full Text: DOI
Gomilko, Oleksandr; Karp, Dmitry B.; Lin, Minghua; Ziȩtak, Krystyna Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix \(p\)th root. (English) Zbl 1251.65057 J. Comput. Appl. Math. 236, No. 17, 4410-4420 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 33F05 15A24 65F10 41A21 15A16 PDFBibTeX XMLCite \textit{O. Gomilko} et al., J. Comput. Appl. Math. 236, No. 17, 4410--4420 (2012; Zbl 1251.65057) Full Text: DOI
Greco, Federico; Iannazzo, Bruno; Poloni, Federico The Padé iterations for the matrix sign function and their reciprocals are optimal. (English) Zbl 1233.65037 Linear Algebra Appl. 436, No. 3, 472-477 (2012). Reviewer: Alyson Reeves (Bowie) MSC: 65H04 65F30 65E05 41A21 30C15 PDFBibTeX XMLCite \textit{F. Greco} et al., Linear Algebra Appl. 436, No. 3, 472--477 (2012; Zbl 1233.65037) Full Text: DOI arXiv
Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P. Efficient orthogonal matrix polynomial based method for computing matrix exponential. (English) Zbl 1211.65052 Appl. Math. Comput. 217, No. 14, 6451-6463 (2011). MSC: 65F30 15A16 34A30 65L05 PDFBibTeX XMLCite \textit{J. Sastre} et al., Appl. Math. Comput. 217, No. 14, 6451--6463 (2011; Zbl 1211.65052) Full Text: DOI Link
Al-Mohy, Awad H.; Higham, Nicholas J. The complex step approximation to the Fréchet derivative of a matrix function. (English) Zbl 1188.65054 Numer. Algorithms 53, No. 1, 133-148 (2010). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 15A60 65F35 PDFBibTeX XMLCite \textit{A. H. Al-Mohy} and \textit{N. J. Higham}, Numer. Algorithms 53, No. 1, 133--148 (2010; Zbl 1188.65054) Full Text: DOI
Laszkiewicz, Beata; Ziȩtak, Krystyna A Padé family of iterations for the matrix sector function and the matrix \(p\)th root. (English) Zbl 1224.65123 Numer. Linear Algebra Appl. 16, No. 11-12, 951-970 (2009). MSC: 65F60 15A16 15A24 65F30 PDFBibTeX XMLCite \textit{B. Laszkiewicz} and \textit{K. Ziȩtak}, Numer. Linear Algebra Appl. 16, No. 11--12, 951--970 (2009; Zbl 1224.65123) Full Text: DOI