Verified computation for the matrix principal logarithm

Two iterative algorithms are proposed for numerically computing an interval matrix containing the matrix principal logarithm. The first algorithm is based on a numerical spectral decomposition and requires only cubic complexity per iteration. The second algorithm is based on a numerical Jordan decom...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 569; pp. 38 - 61
Main Author Miyajima, Shinya
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.05.2019
American Elsevier Company, Inc
Subjects
Algorithms
Complexity
Iterative algorithms
Iterative methods
Linear algebra
Matrix logarithm
Principal logarithm
Verified computation
15A16
65F60
65G20
Matrix logarithm
Verified computation
Principal logarithm
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Summary:Two iterative algorithms are proposed for numerically computing an interval matrix containing the matrix principal logarithm. The first algorithm is based on a numerical spectral decomposition and requires only cubic complexity per iteration. The second algorithm is based on a numerical Jordan decomposition and applicable even for defective matrices. The complexity per iteration of the second algorithm is quartic.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.01.008