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

• Published in: Linear & multilinear algebra Vol. 63; no. 8; pp. 1553 - 1567
• Main Author: Stanimirovic, Ivan P
• Format: Journal Article
• Language: English
• Published: 03.08.2015
• Subjects: Algebra; Algorithms; Computation; Decomposition; Polynomial matrices; Polynomials; Roots
• DOI: 10.1080/03081087.2014.952897
• ISSN: 0308-1087

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.