×

zbMATH — the first resource for mathematics

Accurate and efficient matrix exponential computation. (English) Zbl 1291.65139
Summary: This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential. A Matlab version of the new algorithm is provided and compared with Padé state-of-the-art algorithms obtaining higher accuracy in the majority of tests at similar or even lower cost.

MSC:
65F30 Other matrix algorithms (MSC2010)
65F35 Numerical computation of matrix norms, conditioning, scaling
65F60 Numerical computation of matrix exponential and similar matrix functions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1137/09074721X · Zbl 1194.15021 · doi:10.1137/09074721X
[2] DOI: 10.1016/0024-3795(94)00190-1 · Zbl 0851.65024 · doi:10.1016/0024-3795(94)00190-1
[3] S. Blackford and J. Dongarra,Installation guide for LAPACK, LAPACK Working Note 411, Department of Computer Science, University of Tenessee, 1999.
[4] DOI: 10.1016/S0024-3795(00)00042-2 · Zbl 0958.65050 · doi:10.1016/S0024-3795(00)00042-2
[5] DOI: 10.1023/A:1014071202885 · Zbl 0992.65042 · doi:10.1023/A:1014071202885
[6] DOI: 10.1007/s101070100263 · Zbl 1049.90004 · doi:10.1007/s101070100263
[7] C. Fassino,Computation of matrix functions, Ph.D. thesis TD-7/93, Università di Pisa, Genova, 1993.
[8] DOI: 10.1137/1.9780898718027 · Zbl 1011.65010 · doi:10.1137/1.9780898718027
[9] DOI: 10.1137/04061101X · Zbl 1081.65037 · doi:10.1137/04061101X
[10] DOI: 10.1137/1.9780898717778 · Zbl 1167.15001 · doi:10.1137/1.9780898717778
[11] DOI: 10.1137/S0895479899356080 · Zbl 0959.65061 · doi:10.1137/S0895479899356080
[12] DOI: 10.1137/S00361445024180 · Zbl 1030.65029 · doi:10.1137/S00361445024180
[13] DOI: 10.1137/0202007 · Zbl 0262.65033 · doi:10.1137/0202007
[14] DOI: 10.1016/j.mcm.2010.12.049 · Zbl 1235.65042 · doi:10.1016/j.mcm.2010.12.049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.