Frommer, Andreas; Hashemi, Behnam Computing enclosures for the matrix exponential. (English) Zbl 07301505 SIAM J. Matrix Anal. Appl. 41, No. 4, 1674-1703 (2020). MSC: 65F60 65F30 65G20 PDF BibTeX XML Cite \textit{A. Frommer} and \textit{B. Hashemi}, SIAM J. Matrix Anal. Appl. 41, No. 4, 1674--1703 (2020; Zbl 07301505) Full Text: DOI
Sastre, J.; Ibáñez, J.; Defez, E. Boosting the computation of the matrix exponential. (English) Zbl 1429.65093 Appl. Math. Comput. 340, 206-220 (2019). MSC: 65F60 15A16 PDF BibTeX XML Cite \textit{J. Sastre} et al., Appl. Math. Comput. 340, 206--220 (2019; Zbl 1429.65093) Full Text: DOI
Fasi, Massimiliano; Higham, Nicholas J. An arbitrary precision scaling and squaring algorithm for the matrix exponential. (English) Zbl 1437.65033 SIAM J. Matrix Anal. Appl. 40, No. 4, 1233-1256 (2019). MSC: 65F60 15A16 PDF BibTeX XML Cite \textit{M. Fasi} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 40, No. 4, 1233--1256 (2019; Zbl 1437.65033) Full Text: DOI
Defez, Emilio; Ibáñez, Javier; Peinado, Jesús; Sastre, Jorge; Alonso-Jordá, Pedro An efficient and accurate algorithm for computing the matrix cosine based on new Hermite approximations. (English) Zbl 06997503 J. Comput. Appl. Math. 348, 1-13 (2019). MSC: 94 65 PDF BibTeX XML Cite \textit{E. Defez} et al., J. Comput. Appl. Math. 348, 1--13 (2019; Zbl 06997503) Full Text: DOI
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 PDF BibTeX XML Cite \textit{M. Caliari} and \textit{F. Zivcovich}, J. Comput. Appl. Math. 346, 532--548 (2019; Zbl 1452.65082) Full Text: DOI
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 PDF BibTeX XML Cite \textit{E. Defez} et al., J. Comput. Appl. Math. 337, 354--365 (2018; Zbl 1398.65091) Full Text: DOI
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 PDF BibTeX XML Cite \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
Alonso, Pedro; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Defez, Emilio Efficient and accurate algorithms for computing matrix trigonometric functions. (English) Zbl 1416.65126 J. Comput. Appl. Math. 309, 325-332 (2017). MSC: 65F60 15A16 65Y05 PDF BibTeX XML Cite \textit{P. Alonso} et al., J. Comput. Appl. Math. 309, 325--332 (2017; Zbl 1416.65126) Full Text: DOI
Nakamura, Shinsuke; Ozawa, Kazufumi; Hirota, Chiaki Scaling and modified squaring method for the matrix exponential. (English) Zbl 07037408 JSIAM Lett. 8, 65-68 (2016). MSC: 65 41 PDF BibTeX XML Cite \textit{S. Nakamura} et al., JSIAM Lett. 8, 65--68 (2016; Zbl 07037408) Full Text: DOI
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 PDF BibTeX XML Cite \textit{S. Güttel} and \textit{Y. Nakatsukasa}, SIAM J. Matrix Anal. Appl. 37, No. 1, 145--170 (2016; Zbl 1382.65125) Full Text: DOI
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 PDF BibTeX XML Cite \textit{P. Ruiz} et al., J. Comput. Appl. Math. 291, 370--379 (2016; Zbl 1329.65092) Full Text: DOI
Bader, Philipp; Blanes, Sergio; Seydaoğlu, Muaz The scaling, splitting, and squaring method for the exponential of perturbed matrices. (English) Zbl 1328.65097 SIAM J. Matrix Anal. Appl. 36, No. 2, 594-614 (2015). MSC: 65F30 65F60 PDF BibTeX XML Cite \textit{P. Bader} et al., SIAM J. Matrix Anal. Appl. 36, No. 2, 594--614 (2015; Zbl 1328.65097) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{J. Sastre} et al., SIAM J. Sci. Comput. 37, No. 1, A439--A455 (2015; Zbl 1315.65046) Full Text: DOI
Wang, Chengshan; Fu, Xiaopeng; Li, Peng; Wu, Jianzhong Accurate dense output formula for exponential integrators using the scaling and squaring method. (English) Zbl 1315.65065 Appl. Math. Lett. 43, 101-107 (2015). MSC: 65L05 34A34 65L04 PDF BibTeX XML Cite \textit{C. Wang} et al., Appl. Math. Lett. 43, 101--107 (2015; Zbl 1315.65065) Full Text: DOI
Lu, Chengbo The computations of the logarithms of several classes of circulant matrices. (Chinese. English summary) Zbl 1313.65107 J. Zhejiang Univ., Sci. Ed. 41, No. 4, 367-372 (2014). MSC: 65F60 15A24 15B57 PDF BibTeX XML Cite \textit{C. Lu}, J. Zhejiang Univ., Sci. Ed. 41, No. 4, 367--372 (2014; Zbl 1313.65107) Full Text: DOI
Shao, Meiyue; Gao, Weiguo; Xue, Jungong Aggressively truncated Taylor series method for accurate computation of exponentials of essentially nonnegative matrices. (English) Zbl 1309.65051 SIAM J. Matrix Anal. Appl. 35, No. 2, 317-338 (2014). Reviewer: Liu Xinguo (Qingdao) MSC: 65F60 15B48 PDF BibTeX XML Cite \textit{M. Shao} et al., SIAM J. Matrix Anal. Appl. 35, No. 2, 317--338 (2014; Zbl 1309.65051) Full Text: DOI
Aprahamian, Mary; Higham, Nicholas J. The matrix unwinding function, with an application to computing the matrix exponential. (English) Zbl 1300.65024 SIAM J. Matrix Anal. Appl. 35, No. 1, 88-109 (2014). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 65F35 15A24 65F60 PDF BibTeX XML Cite \textit{M. Aprahamian} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 35, No. 1, 88--109 (2014; Zbl 1300.65024) Full Text: DOI
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 PDF BibTeX XML Cite \textit{J. Sastre} et al., Int. J. Comput. Math. 91, No. 1, 97--112 (2014; Zbl 1291.65139) Full Text: DOI
Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D. Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. (English) Zbl 1362.65051 SIAM J. Sci. Comput. 35, No. 4, C394-C410 (2013). MSC: 65F60 65F30 65F35 PDF BibTeX XML Cite \textit{A. H. Al-Mohy} et al., SIAM J. Sci. Comput. 35, No. 4, C394--C410 (2013; Zbl 1362.65051) Full Text: DOI
Lu, Chengbo On the logarithms of circulant matrices. (English) Zbl 1287.65037 J. Comput. Anal. Appl. 15, No. 3, 402-412 (2013). Reviewer: João R. Cardoso (Coimbra) MSC: 65F60 15A16 65F35 PDF BibTeX XML Cite \textit{C. Lu}, J. Comput. Anal. Appl. 15, No. 3, 402--412 (2013; Zbl 1287.65037)
Al-Mohy, Awad H. A more accurate Briggs method for the logarithm. (English) Zbl 1236.65018 Numer. Algorithms 59, No. 3, 393-402 (2012). MSC: 65D20 33B10 33F05 26A09 PDF BibTeX XML Cite \textit{A. H. Al-Mohy}, Numer. Algorithms 59, No. 3, 393--402 (2012; Zbl 1236.65018) 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 PDF BibTeX XML Cite \textit{J. Sastre} et al., Math. Comput. Modelling 54, No. 7--8, 1835--1840 (2011; Zbl 1235.65042) Full Text: DOI
Tao, Molei; Owhadi, Houman; Marsden, Jerrold E. From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials. (English) Zbl 1243.65149 AMRX, Appl. Math. Res. Express 2011, 242-280 (2011). Reviewer: Kevin Burrage (Brisbane) MSC: 65P10 37M15 PDF BibTeX XML Cite \textit{M. Tao} et al., AMRX, Appl. Math. Res. Express 2011, 242--280 (2011; Zbl 1243.65149) Full Text: DOI arXiv
Al-Mohy, Awad H.; Higham, Nicholas J. A new scaling and squaring algorithm for the matrix exponential. (English) Zbl 1194.15021 SIAM J. Matrix Anal. Appl. 31(2009), No. 3, 970-989 (2010). MSC: 15A60 65F30 PDF BibTeX XML Cite \textit{A. H. Al-Mohy} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 31, No. 3, 970--989 (2010; Zbl 1194.15021) Full Text: DOI
Cardoso, João R.; Silva Leite, F. Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices. (English) Zbl 1185.65070 J. Comput. Appl. Math. 233, No. 11, 2867-2875 (2010). MSC: 65F30 15A16 15B57 15B10 15A12 65F35 PDF BibTeX XML Cite \textit{J. R. Cardoso} and \textit{F. Silva Leite}, J. Comput. Appl. Math. 233, No. 11, 2867--2875 (2010; Zbl 1185.65070) Full Text: DOI
Higham, Nicholas J. The scaling and squaring method for the matrix exponential revisited. (English) Zbl 1178.65040 SIAM Rev. 51, No. 4, 747-764 (2009). MSC: 65F30 PDF BibTeX XML Cite \textit{N. J. Higham}, SIAM Rev. 51, No. 4, 747--764 (2009; Zbl 1178.65040) Full Text: DOI
Al-Mohy, Awad H.; Higham, Nicholas J. Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. (English) Zbl 1180.65049 SIAM J. Matrix Anal. Appl. 30, No. 4, 1639-1657 (2009). Reviewer: Lubomír Bakule (Praha) MSC: 65F30 15A60 65J05 15A16 65F35 PDF BibTeX XML Cite \textit{A. H. Al-Mohy} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 30, No. 4, 1639--1657 (2009; Zbl 1180.65049) Full Text: DOI
Skaflestad, B.; Wright, W. M. The scaling and modified squaring method for matrix functions related to the exponential. (English) Zbl 1160.65034 Appl. Numer. Math. 59, No. 3-4, 783-799 (2009). MSC: 65L05 34A34 PDF BibTeX XML Cite \textit{B. Skaflestad} and \textit{W. M. Wright}, Appl. Numer. Math. 59, No. 3--4, 783--799 (2009; Zbl 1160.65034) Full Text: DOI
Guo, Chun-Hua; Higham, Nicholas J. A Schur-Newton method for the matrix \(p\)th root and its inverse. (English) Zbl 1128.65030 SIAM J. Matrix Anal. Appl. 28, No. 3, 788-804 (2006). Reviewer: Lubomír Bakule (Praha) MSC: 65F30 15A18 15B51 15A24 PDF BibTeX XML Cite \textit{C.-H. Guo} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 28, No. 3, 788--804 (2006; Zbl 1128.65030) Full Text: DOI
Cardoso, João R.; Silva Leite, F. Padé and Gregory error estimates for the logarithm of block triangular matrices. (English) Zbl 1094.65037 Appl. Numer. Math. 56, No. 2, 253-267 (2006). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F30 15A24 41A21 PDF BibTeX XML Cite \textit{J. R. Cardoso} and \textit{F. Silva Leite}, Appl. Numer. Math. 56, No. 2, 253--267 (2006; Zbl 1094.65037) Full Text: DOI
Higham, Nicholas J. The scaling and squaring method for the matrix exponential revisited. (English) Zbl 1081.65037 SIAM J. Matrix Anal. Appl. 26, No. 4, 1179-1193 (2005). MSC: 65F30 PDF BibTeX XML Cite \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 26, No. 4, 1179--1193 (2005; Zbl 1081.65037) Full Text: DOI
Fung, T. C. Computation of the matrix exponential and its derivatives by scaling and squaring. (English) Zbl 1048.65040 Int. J. Numer. Methods Eng. 59, No. 10, 1273-1286 (2004). MSC: 65F30 15A54 PDF BibTeX XML Cite \textit{T. C. Fung}, Int. J. Numer. Methods Eng. 59, No. 10, 1273--1286 (2004; Zbl 1048.65040) Full Text: DOI
Cheng, Sheung Hun; Higham, Nicholas J.; Kenney, Charles S.; Laub, Alan J. Approximating the logarithm of a matrix to specified accuracy. (English) Zbl 0989.65057 SIAM J. Matrix Anal. Appl. 22, No. 4, 1112-1125 (2001). Reviewer: Michael Tsatsomeros (Pullman) MSC: 65F30 15A24 PDF BibTeX XML Cite \textit{S. H. Cheng} et al., SIAM J. Matrix Anal. Appl. 22, No. 4, 1112--1125 (2001; Zbl 0989.65057) Full Text: DOI
Higham, Nicholas J. Evaluating Padé approximants of the matrix logarithm. (English) Zbl 0989.65054 SIAM J. Matrix Anal. Appl. 22, No. 4, 1126-1135 (2001). Reviewer: Michael Tsatsomeros (Pullman) MSC: 65F30 15A24 PDF BibTeX XML Cite \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 22, No. 4, 1126--1135 (2001; Zbl 0989.65054) Full Text: DOI
Zhang, Hongwu; Zhong, Wanxie Discussion about numerical computation of the matrix exponential. (Chinese. English summary) Zbl 0979.65036 J. Dalian Univ. Technol. 40, No. 5, 522-525 (2000). MSC: 65F30 65Y20 PDF BibTeX XML Cite \textit{H. Zhang} and \textit{W. Zhong}, J. Dalian Univ. Technol. 40, No. 5, 522--525 (2000; Zbl 0979.65036)
Dieci, Luca; Papini, Alessandra Padé approximation for the exponential of a block triangular matrix. (English) Zbl 0958.65050 Linear Algebra Appl. 308, No. 1-3, 183-202 (2000). Reviewer: Juan Pedro Milaszewicz (Buenos Aires) MSC: 65F30 65F35 PDF BibTeX XML Cite \textit{L. Dieci} and \textit{A. Papini}, Linear Algebra Appl. 308, No. 1--3, 183--202 (2000; Zbl 0958.65050) Full Text: DOI
Najfeld, Igor; Havel, Timothy F. Derivatives of the matrix exponential and their computation. (English) Zbl 0839.15004 Adv. Appl. Math. 16, No. 3, 321-375 (1995). Reviewer: V.Prepeliţă (Bucureşti) MSC: 15A15 65F30 15A90 PDF BibTeX XML Cite \textit{I. Najfeld} and \textit{T. F. Havel}, Adv. Appl. Math. 16, No. 3, 321--375 (1995; Zbl 0839.15004) Full Text: DOI
Carroll, John On the implementation of a matricial exponentially fitted scheme for the numerical solution of stiff initial-value problems. (English) Zbl 0824.65047 Ann. Numer. Math. 1, No. 1-4, 377-383 (1994). Reviewer: Th.Sonar (Göttingen) MSC: 65L05 65L06 34A34 34E13 PDF BibTeX XML Cite \textit{J. Carroll}, Ann. Numer. Math. 1, No. 1--4, 377--383 (1994; Zbl 0824.65047)
Melloy, Brian J.; Bennett, G. Kemble Computing the exponential of an intensity matrix. (English) Zbl 0781.65036 J. Comput. Appl. Math. 46, No. 3, 405-413 (1993). Reviewer: P.Polcar (Brno) MSC: 65F30 65D20 60J25 PDF BibTeX XML Cite \textit{B. J. Melloy} and \textit{G. K. Bennett}, J. Comput. Appl. Math. 46, No. 3, 405--413 (1993; Zbl 0781.65036) Full Text: DOI
Codenotti, B.; Fassino, C. Error analysis of two algorithms for the computation of the matrix exponential. (English) Zbl 0778.65033 Calcolo 29, No. 1-2, 1-31 (1992). Reviewer: F.Uhlig (Auburn) MSC: 65F30 65F35 PDF BibTeX XML Cite \textit{B. Codenotti} and \textit{C. Fassino}, Calcolo 29, No. 1--2, 1--31 (1992; Zbl 0778.65033) Full Text: DOI
Kenney, Charles; Laub, Alan J. Padé error estimates for the logarithm of a matrix. (English) Zbl 0685.65036 Int. J. Control 50, No. 3, 707-730 (1989). Reviewer: M.Kono MSC: 65F30 41A21 41A25 PDF BibTeX XML Cite \textit{C. Kenney} and \textit{A. J. Laub}, Int. J. Control 50, No. 3, 707--730 (1989; Zbl 0685.65036) Full Text: DOI
Bochev, Pavel; Markov, Svetoslav A self-validating numerical method for the matrix exponential. (English) Zbl 0685.65035 Computing 43, No. 1, 59-72 (1989). Reviewer: H.-J.Sprengel MSC: 65F30 65G30 15A60 41A21 PDF BibTeX XML Cite \textit{P. Bochev} and \textit{S. Markov}, Computing 43, No. 1, 59--72 (1989; Zbl 0685.65035) Full Text: DOI
Evans, D. J.; Margaritis, K. Systolic computation of the matrix exponential and other matrix functions. (English) Zbl 0658.65042 Int. J. Comput. Math. 25, No. 3-4, 345-358 (1988). Reviewer: A.de Castro MSC: 65F30 65D20 15A60 PDF BibTeX XML Cite \textit{D. J. Evans} and \textit{K. Margaritis}, Int. J. Comput. Math. 25, No. 3--4, 345--358 (1988; Zbl 0658.65042) Full Text: DOI
Serbin, Steven M.; Blalock, Sybil A. An algorithm for computing the matrix cosine. (English) Zbl 0445.65023 SIAM J. Sci. Stat. Comput. 1, 198-204 (1980). MSC: 65F30 15A15 41A45 34A12 PDF BibTeX XML Cite \textit{S. M. Serbin} and \textit{S. A. Blalock}, SIAM J. Sci. Stat. Comput. 1, 198--204 (1980; Zbl 0445.65023) Full Text: DOI