Fast enclosure for a matrix inverse square root

A fast algorithm for computing an interval matrix containing the inverse square root of an n×n matrix A is proposed. This algorithm utilizes numerical spectral decomposition of A and requires only O(n3) operations. The principal property and uniqueness of the contained inverse square root can moreov...

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Vydané v:Linear algebra and its applications Ročník 467; s. 116 - 135
Hlavný autor: Miyajima, Shinya
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.02.2015
Predmet:
Matrix function
Matrix inverse square root
Numerical enclosure
Verified computation
65G50
65G20
Numerical enclosure
65F30
Matrix inverse square root
Matrix function
Verified computation
65F05
ISSN:0024-3795, 1873-1856
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Popis
Shrnutí:A fast algorithm for computing an interval matrix containing the inverse square root of an n×n matrix A is proposed. This algorithm utilizes numerical spectral decomposition of A and requires only O(n3) operations. The principal property and uniqueness of the contained inverse square root can moreover be verified by the proposed algorithm. Numerical results show the effectiveness and efficiency of this algorithm.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2014.11.007