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High performance computing of the matrix exponential. (English) Zbl 1329.65092
Summary: This work presents a new algorithm for matrix exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the new simplified algorithm has been compared with the original algorithm, providing similar results in terms of accuracy, but reducing processing time. It has also been compared with two state-of-the-art implementations based on Padé approximations, one commercial and the other implemented in Matlab, getting better accuracy and processing time results in the majority of cases.

MSC:
65F60 Numerical computation of matrix exponential and similar matrix functions
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[1] Moler, C. B.; Loan, C. V., Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45, 3-49, (2003) · Zbl 1030.65029
[2] Higham, N. J., Functions of matrices: theory and computation, (2008), Society for Industrial and Applied Mathematics Philadelphia, PA, USA · Zbl 1167.15001
[3] Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P., New scaling-squaring Taylor algorithms for computing the matrix exponential, SIAM J. Sci. Comput., 37-1, A439-A455, (2015) · Zbl 1315.65046
[4] Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P., Accurate matrix exponential computation to solve coupled differential models in engineering, Math. Comput. Model., 54, 1835-1840, (2011) · Zbl 1235.65042
[5] Al-Mohy, A. H.; Higham, N. J., A new scaling and squaring algorithm for the matrix exponential, SIAM J. Matrix Anal. Appl., 31, 3, 970-989, (2009) · Zbl 1194.15021
[6] Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P., Accurate and efficient matrix exponential computation, Int. J. Comput. Math., 91, 1, 97-112, (2014) · Zbl 1291.65139
[7] NAG Library Function Document, http://www.nag.co.uk/numeric/cl/nagdoc_cl23/html/F01/f01ecc.html.
[8] Al-Mohy, A. H.; Higham, N. J., Computing the action of the matrix exponential, with an application to exponential integrators, SIAM J. Sci. Comput., 33, 2, 488-511, (2011) · Zbl 1234.65028
[9] Higham, J.; Tisseur, F., A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra, SIAM J. Matrix Anal. Appl., 21, 1185-1201, (2000) · Zbl 0959.65061
[10] N.J. Higham, The Matrix Computation Toolbox, http://www.ma.man.ac.uk/ higham/mctoolbox/.
[11] Higham, N. J., The scaling and squaring method for the matrix exponential revisited, SIAM J. Matrix Anal. Appl., 26, 4, 1179-1193, (2005) · Zbl 1081.65037
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