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A self-validating numerical method for the matrix exponential. (English) Zbl 0685.65035

An algorithm is presented which produces highly accurate and automatically verified bounds for \(\exp (A)=\sum^{\infty}_{k=0}A^ k/k!\) where A is a real \(n\times n\) matrix. The method is based on interval analysis techniques and the iterative defect correction principle. The “scaling and squaring” approach is realized by the Padé approximations and safe error monitoring. Finally there are three examples \((n=2\), \(n=3)\) in order to compare the numerical results with the results by conventional floating-point computations.
Reviewer: H.-J.Sprengel

MSC:

65F30 Other matrix algorithms (MSC2010)
65G30 Interval and finite arithmetic
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
41A21 Padé approximation

Software:

HIFICOMP
PDFBibTeX XMLCite
Full Text: DOI

References:

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