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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Bibliographic Details
Published in:Linear algebra and its applications Vol. 467; pp. 116 - 135
Main Author: Miyajima, Shinya
Format: Journal Article
Language:English
Published: Elsevier Inc 15.02.2015
Subjects:
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
Online Access:Get full text
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Summary: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