Atlantis Press Paper Details: A comparative study of matrix inversion by recursive algorithms through single and double bordering

In this paper we have derived single and double bordering methods for computation of the inverse of a matrix. The performance of these methods is compared with some existing methods . We conclude the following: For a general nonsingular matrix, both single and double bordering methods are superior to the existing factorization method, while the double bordering method is superior compared to the single bordering method. For example, n=31 (odd), the factorization, single and double bordering methods respectively have the operational counts as 60109,57961,56806. For n=30 (even), the factorization, single and double bordering methods respectively have the operational counts as 54495,52230,51405. For a PDS matrix, double bordering method is much superior compared to the single bordering and Cholesky methods. For a large n, the operational counts for double bordering, single bordering, and Cholesky methods are respectively of orders and (approximately). For example, n=31 (odd), the operational counts for double bordering, single bordering and Cholesky method respectively are 29116,38781,50158. For n=31 (odd), the operational counts for double bordering, single bordering and Cholesky method respectively are 26370,35120,45475.

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title:		A comparative study of matrix inversion by recursive algorithms through single and double bordering
publication:		JCIS-2006 Proceedings
part of series:		Advances in Intelligent Systems Research
ISBN:		978-90-78677-01-7
ISSN:		1951-6851
DOI:		doi:10.2991/jcis.2006.249 (how to use a DOI)
author(s):		Bhavanam Rami Reddy, Ramabhadra Prof. I. Ramabhadra Sarma
publication date:		October 2006
keywords:		centrosymmetric matrix, bordering, operational count, cholesky decomposition
abstract:		In this paper we have derived single and double bordering methods for computation of the inverse of a matrix. The performance of these methods is compared with some existing methods . We conclude the following: For a general nonsingular matrix, both single and double bordering methods are superior to the existing factorization method, while the double bordering method is superior compared to the single bordering method. For example, n=31 (odd), the factorization, single and double bordering methods respectively have the operational counts as 60109,57961,56806. For n=30 (even), the factorization, single and double bordering methods respectively have the operational counts as 54495,52230,51405. For a PDS matrix, double bordering method is much superior compared to the single bordering and Cholesky methods. For a large n, the operational counts for double bordering, single bordering, and Cholesky methods are respectively of orders and (approximately). For example, n=31 (odd), the operational counts for double bordering, single bordering and Cholesky method respectively are 29116,38781,50158. For n=31 (odd), the operational counts for double bordering, single bordering and Cholesky method respectively are 26370,35120,45475.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		JCIS06-CSI-83.pdf (2641 K)