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
Li, Dongping; Yang, Siyu; Lan, Jiamei Efficient and accurate computation for the \(\varphi\)-functions arising from exponential integrators. (English) Zbl 1485.65050 Calcolo 59, No. 1, Paper No. 11, 24 p. (2022). MSC: 65F60 65L05 PDFBibTeX XMLCite \textit{D. Li} et al., Calcolo 59, No. 1, Paper No. 11, 24 p. (2022; Zbl 1485.65050) Full Text: DOI arXiv
Caliari, M.; Zivcovich, F. On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm. (English) Zbl 1452.65082 J. Comput. Appl. Math. 346, 532-548 (2019). MSC: 65F60 15A16 PDFBibTeX XMLCite \textit{M. Caliari} and \textit{F. Zivcovich}, J. Comput. Appl. Math. 346, 532--548 (2019; Zbl 1452.65082) Full Text: DOI
Costabile, F. A.; Gualtieri, M. I.; Napoli, A.; Altomare, M. Odd and even Lidstone-type polynomial sequences. I: Basic topics. (English) Zbl 1435.41031 Adv. Difference Equ. 2018, Paper No. 299, 26 p. (2018). MSC: 41A58 11B83 PDFBibTeX XMLCite \textit{F. A. Costabile} et al., Adv. Difference Equ. 2018, Paper No. 299, 26 p. (2018; Zbl 1435.41031) Full Text: DOI
Al-Mohy, Awad H. A truncated Taylor series algorithm for computing the action of trigonometric and hyperbolic matrix functions. (English) Zbl 1391.15031 SIAM J. Sci. Comput. 40, No. 3, A1696-A1713 (2018). MSC: 15A16 15A60 65F30 PDFBibTeX XMLCite \textit{A. H. Al-Mohy}, SIAM J. Sci. Comput. 40, No. 3, A1696--A1713 (2018; Zbl 1391.15031) Full Text: DOI arXiv
Defez, Emilio; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Alonso, Pedro A new efficient and accurate spline algorithm for the matrix exponential computation. (English) Zbl 1398.65091 J. Comput. Appl. Math. 337, 354-365 (2018). MSC: 65F60 15A16 65D07 65Y10 PDFBibTeX XMLCite \textit{E. Defez} et al., J. Comput. Appl. Math. 337, 354--365 (2018; Zbl 1398.65091) Full Text: DOI Link
Fischer, Thomas M. On the algorithm by Al-Mohy and Higham for computing the action of the matrix exponential: a posteriori roundoff error estimation. (English) Zbl 1372.65137 Linear Algebra Appl. 531, 141-168 (2017). MSC: 65F60 65G50 PDFBibTeX XMLCite \textit{T. M. Fischer}, Linear Algebra Appl. 531, 141--168 (2017; Zbl 1372.65137) Full Text: DOI
Higham, Nicholas J.; Kandolf, Peter Computing the action of trigonometric and hyperbolic matrix functions. (English) Zbl 1365.65135 SIAM J. Sci. Comput. 39, No. 2, A613-A627 (2017). MSC: 65F60 PDFBibTeX XMLCite \textit{N. J. Higham} and \textit{P. Kandolf}, SIAM J. Sci. Comput. 39, No. 2, A613--A627 (2017; Zbl 1365.65135) Full Text: DOI arXiv
Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan The Leja method revisited: backward error analysis for the matrix exponential. (English) Zbl 1339.65061 SIAM J. Sci. Comput. 38, No. 3, A1639-A1661 (2016). MSC: 65F60 65D05 PDFBibTeX XMLCite \textit{M. Caliari} et al., SIAM J. Sci. Comput. 38, No. 3, A1639--A1661 (2016; Zbl 1339.65061) Full Text: DOI arXiv
Ruiz, P.; Sastre, J.; Ibáñez, J.; Defez, E. High performance computing of the matrix exponential. (English) Zbl 1329.65092 J. Comput. Appl. Math. 291, 370-379 (2016). MSC: 65F60 PDFBibTeX XMLCite \textit{P. Ruiz} et al., J. Comput. Appl. Math. 291, 370--379 (2016; Zbl 1329.65092) Full Text: DOI
Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P. New scaling-squaring Taylor algorithms for computing the matrix exponential. (English) Zbl 1315.65046 SIAM J. Sci. Comput. 37, No. 1, A439-A455 (2015). MSC: 65F60 PDFBibTeX XMLCite \textit{J. Sastre} et al., SIAM J. Sci. Comput. 37, No. 1, A439--A455 (2015; Zbl 1315.65046) Full Text: DOI Link
Sastre, J.; Ibáñez, J.; Ruiz, P.; Defez, E. Accurate and efficient matrix exponential computation. (English) Zbl 1291.65139 Int. J. Comput. Math. 91, No. 1, 97-112 (2014). MSC: 65F30 65F35 65F60 PDFBibTeX XMLCite \textit{J. Sastre} et al., Int. J. Comput. Math. 91, No. 1, 97--112 (2014; Zbl 1291.65139) Full Text: DOI Link
Rodríguez, Marcos; Barrio, Roberto Reducing rounding errors and achieving Brouwer’s law with Taylor series method. (English) Zbl 1243.65080 Appl. Numer. Math. 62, No. 8, 1014-1024 (2012). MSC: 65L05 34A34 65Y20 65L70 34A25 PDFBibTeX XMLCite \textit{M. Rodríguez} and \textit{R. Barrio}, Appl. Numer. Math. 62, No. 8, 1014--1024 (2012; Zbl 1243.65080) Full Text: DOI
Barrio, R.; Rodríguez, M.; Abad, A.; Serrano, S. Uncertainty propagation or box propagation. (English) Zbl 1235.65092 Math. Comput. Modelling 54, No. 11-12, 2602-2615 (2011). MSC: 65L99 PDFBibTeX XMLCite \textit{R. Barrio} et al., Math. Comput. Modelling 54, No. 11--12, 2602--2615 (2011; Zbl 1235.65092) Full Text: DOI
Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P. Accurate matrix exponential computation to solve coupled differential models in engineering. (English) Zbl 1235.65042 Math. Comput. Modelling 54, No. 7-8, 1835-1840 (2011). MSC: 65F60 15A16 PDFBibTeX XMLCite \textit{J. Sastre} et al., Math. Comput. Modelling 54, No. 7--8, 1835--1840 (2011; Zbl 1235.65042) Full Text: DOI Link
Al-Mohy, Awad H.; Higham, Nicholas J. Computing the action of the matrix exponential, with an application to exponential integrators. (English) Zbl 1234.65028 SIAM J. Sci. Comput. 33, No. 2, 488-511 (2011). Reviewer: Frank Uhlig (Auburn) MSC: 65F60 15A16 65G50 65F35 65L05 34A30 PDFBibTeX XMLCite \textit{A. H. Al-Mohy} and \textit{N. J. Higham}, SIAM J. Sci. Comput. 33, No. 2, 488--511 (2011; Zbl 1234.65028) Full Text: DOI Link
Barrio, R.; Rodríguez, M.; Abad, A.; Blesa, F. Breaking the limits: The Taylor series method. (English) Zbl 1219.65064 Appl. Math. Comput. 217, No. 20, 7940-7954 (2011). MSC: 65L05 34A34 34A25 65L70 34-04 65Y15 PDFBibTeX XMLCite \textit{R. Barrio} et al., Appl. Math. Comput. 217, No. 20, 7940--7954 (2011; Zbl 1219.65064) Full Text: DOI
Hargreaves, Gareth I.; Higham, Nicholas J. Efficient algorithms for the matrix cosine and sine. (English) Zbl 1084.65039 Numer. Algorithms 40, No. 4, 383-400 (2005). MSC: 65F30 65D20 15A24 15A54 PDFBibTeX XMLCite \textit{G. I. Hargreaves} and \textit{N. J. Higham}, Numer. Algorithms 40, No. 4, 383--400 (2005; Zbl 1084.65039) Full Text: DOI Link
Davies, Philip I.; Higham, Nicholas J. A Schur-Parlett algorithm for computing matrix functions. (English) Zbl 1052.65031 SIAM J. Matrix Anal. Appl. 25, No. 2, 464-485 (2003). Reviewer: Raffaella Pavani (Milano) MSC: 65F30 15A24 15A54 PDFBibTeX XMLCite \textit{P. I. Davies} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 25, No. 2, 464--485 (2003; Zbl 1052.65031) Full Text: DOI
Richardson, J. D.; Gray, L. J.; Kaplan, T.; Napier, J. A. L. Regularized spectral multipole BEM for plane elasticity. (English) Zbl 1007.74084 Eng. Anal. Bound. Elem. 25, No. 4-5, 297-311 (2001). Reviewer: Ján Sládek (Bratislava) MSC: 74S15 74B05 PDFBibTeX XMLCite \textit{J. D. Richardson} et al., Eng. Anal. Bound. Elem. 25, No. 4--5, 297--311 (2001; Zbl 1007.74084) Full Text: DOI