Computing A sub(T),S super(2)) inverses of Hermitian matrices via LDL super() decomposition for a square matrix A

A method for the computation of [Image omitted.] inverses of a given matrix [Image omitted.] is derived, based on the full-rank [Image omitted.] decomposition of an appropriate matrix [Image omitted.]. As a corollary, a new method considering the advantages of full-rank [Image omitted.] decompositio...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 63; no. 8; pp. 1553 - 1567
Main Author Stanimirovic, Ivan P
Format Journal Article
LanguageEnglish
Published 03.08.2015
Subjects
Algebra
Algorithms
Computation
Decomposition
Polynomial matrices
Polynomials
Roots
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Summary:A method for the computation of [Image omitted.] inverses of a given matrix [Image omitted.] is derived, based on the full-rank [Image omitted.] decomposition of an appropriate matrix [Image omitted.]. As a corollary, a new method considering the advantages of full-rank [Image omitted.] decomposition is developed. It is then specialized to the set of polynomial matrices. Therefore, an algorithm for efficient symbolic computation of [Image omitted.] inverses of a polynomial matrix is proposed. An additional diagonal matrix [Image omitted.] yields to avoiding the computation of entries containing square roots of polynomials, therefore increasing the algorithm's performances. Some implementation details and comparative processing times to other similar methods are provided, illustrating the algorithm's efficiency.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2014.952897