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Advances in Numerical Analysis
Volume 2011 (2011), Article ID 593548, 6 pages
http://dx.doi.org/10.1155/2011/593548
Research Article

A Generalization of a Class of Matrices: Analytic Inverse and Determinant

Department of Mathematics, University of Patras, 26500 Patras, Greece

Received 29 December 2010; Revised 3 October 2011; Accepted 10 October 2011

Academic Editor: Alfredo Bermudez De Castro

Copyright © 2011 F. N. Valvi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to present the structure of a class of matrices that enables explicit inverse to be obtained. Starting from an already known class of matrices, we construct a Hadamard product that derives the class under consideration. The latter are defined by 4 𝑛 2 parameters, analytic expressions of which provide the elements of the lower Hessenberg form inverse. Recursion formulae of these expressions reduce the arithmetic operations in evaluating the inverse to 𝒪 ( 𝑛 2 ) .