Computing Outer Inverses Using Complete Orthogonal Factorizations

Autor:	Bilall I. Shaini
Rok vydání:	2014
Předmět:	Combinatorics Complex matrix Rank (linear algebra) Singular value decomposition Decomposition (computer science) Triangular matrix Inverse Constant (mathematics) Representation (mathematics) Mathematics
Zdroj:	Journal of Mathematics Research. 6
ISSN:	1916-9809 1916-9795
DOI:	10.5539/jmr.v6n3p91
Popis:	Several full-rank representations of the $A_{T,S}^{(2)}$ inverse of a given constant complex matrix, which are based on various complete orthogonal factorizations, are introduced. Particularly, we introduce a full rank representation based on the Singular Value Decomposition ($SVD$) as well as on a combination of the $QR$ decomposition and the $SVD$ of the triangular matrix produced by the $QR$ decomposition. Furthermore, representations based on the factorizations to a bidiagonal form are defined. The representations arising from reductions to bidiagonal form are applicable to real full row rank matrices. Illustrative numerical examples as well as an extensive numerical study are presented. A comparison of three introduced methods is presented.
Databáze:	OpenAIRE
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