Inversion of analytic matrix functions that are singular at the origin

Konstantin E. Avrachenkov; Moshe Haviv; Phil G. Howlett

doi:10.1137/S0895479898337555

Inversion of analytic matrix functions that are singular at the origin

Konstantin E. Avrachenkov^*, Moshe Haviv, Phil G. Howlett

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

In this paper we study the inversion of an analytic matrix valued function A(z). This problem can also be viewed as an analytic perturbation of the matrix A₀ = A(0). We are mainly interested in the case where A₀ is singular but A(z) has an inverse in some punctured disc around z = 0. It is known that A^-1(z) can be expanded as a Laurent series at the origin. The main purpose of this paper is to provide efficient computational procedures for the coefficients of this series. We demonstrate that the proposed algorithms are computationally superior to symbolic algebra when the order of the pole is small.

Original language	English
Pages (from-to)	1175-1189
Number of pages	15
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	22
Issue number	4
DOIs	https://doi.org/10.1137/S0895479898337555
State	Published - Jan 2001

Keywords

Analytic perturbation
Laurent series
Matrix inversion
Matrix valued functions

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Inversion of analytic matrix functions that are singular at the origin

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Keywords

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