Computational techniques for real logarithms of matrices. (English) Zbl 0870.65036

The art of numerically evaluating matrix functions such as the real logarithm of a given real matrix \(A\) lies in its infancy. This paper investigates and compares potential approaches to the problem of finding a real matrix \(X\) so that \(e^X=A\). The recommended general purpose algorithm of this paper involves a real Schur block-decomposition of \(A\) with eigenvalue grouping, followed by a scaling of the diagonal blocks via matrix square roots and a diagonal Padé approximation, which is the equivalent of an ordinary differential equation solver used for the problem. The paper pays close attention to conditioning and compares its algorithm’s performance to other methods numerically.
Reviewer: F.Uhlig (Auburn)


65F30 Other matrix algorithms (MSC2010)
15A12 Conditioning of matrices
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
65F35 Numerical computation of matrix norms, conditioning, scaling


Full Text: DOI