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A program for the computation of the matrix exponential function using the diagonal Padé approximation. (Russian) Zbl 0554.41001
Degenerate systems of ordinary differential equations, Collect. Artic., Novosibirsk 1982, 91-97 (1982).
[For the entire collection see Zbl 0511.00015.]
An ALGOL program for the computation of the matrix exponential function \(\exp (A)=\sum^{\infty}_{k=0}A^ k/k!\) is given, where A is a constant finite-dimensional matrix with real elements. The problem is reduced to the computation of the diagonal Padé approximants by using R. Ward’s idea [SIAM J. Numer. Anal. 14, 600-610 (1977; Zbl 0363.65031)]. A modification of this idea is presented.
Reviewer: G.L.Litvinov
MSC:
41-04 Software, source code, etc. for problems pertaining to approximations and expansions
41A21 Padé approximation
65F30 Other matrix algorithms (MSC2010)
65D15 Algorithms for approximation of functions
41A20 Approximation by rational functions
65-04 Software, source code, etc. for problems pertaining to numerical analysis