In this work, we consider computing the real logarithm of a real matrix. We pay attention to general conditioning issues, provide careful implementation for several techniques including scaling issues, and finally test and compare the techniques on a number of problems. All things considered, our recommendation for a general purpose method goes to the Schur decomposition approach with eigenvalue grouping, followed by square roots and diagonal Pade approximants of the diagonal blocks. Nonetheless, in some cases, a well-implemented series expansion technique outperformed the other methods. We have also analyzed and implemented a novel method to estimate the Frechet derivative of the log, which proved very successful for condition estimation.

Computational techniques for real logarithms of matrices / B. MORINI; A. PAPINI; L. DIECI. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - STAMPA. - 17:(1996), pp. 570-593. [10.1137/S0895479894273614]

Computational techniques for real logarithms of matrices

MORINI, BENEDETTA;PAPINI, ALESSANDRA;
1996

Abstract

In this work, we consider computing the real logarithm of a real matrix. We pay attention to general conditioning issues, provide careful implementation for several techniques including scaling issues, and finally test and compare the techniques on a number of problems. All things considered, our recommendation for a general purpose method goes to the Schur decomposition approach with eigenvalue grouping, followed by square roots and diagonal Pade approximants of the diagonal blocks. Nonetheless, in some cases, a well-implemented series expansion technique outperformed the other methods. We have also analyzed and implemented a novel method to estimate the Frechet derivative of the log, which proved very successful for condition estimation.
1996
17
570
593
B. MORINI; A. PAPINI; L. DIECI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/307257
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