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2010•Journal of Anhui UniversityRequires access

A fast algorithm for the Moore-Penrose inverse of symmetric Loewner matrix

Qiujuan Tong

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Abstract

Symmetric Loewner-type matrix has broad applications in natural sciences and engineering technologies.Many of the issues were summarized for the sake of symmetric Loewner(type) matrix and its correlation matrix algebraic problem.This article presented a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studied its inverse.Its computation complexity was O(mn)+O(n2),but it was O(mn2)+O(n3) by using L+=(LTL)-1LT.Experimental results also showed that the former in terms of time and accuracy were better than the latter.

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Symmetric Loewner-type matrix has broad applications in natural sciences and engineering technologies.Many of the issues were summarized for the sake of symmetric Loewner(type) matrix and its correlation matrix algebraic problem.This article presented a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studied its inverse.Its computation complexity was O(mn)+O(n2),but it was O(mn2)+O(n3) by using L+=(LTL)-1LT.Experimental results also showed that the former in terms of time and accuracy were better than the latter.

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Available abstract

Symmetric Loewner-type matrix has broad applications in natural sciences and engineering technologies.Many of the issues were summarized for the sake of symmetric Loewner(type) matrix and its correlation matrix algebraic problem.This article presented a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studied its inverse.Its computation complexity was O(mn)+O(n2),but it was O(mn2)+O(n3) by using L+=(LTL)-1LT.Experimental results also showed that the former in terms of time and accuracy were better than the latter.

Key concepts: Inverse, Mathematics, Matrix (chemical analysis), Symmetric matrix, Block matrix, Combinatorics, Moore–Penrose pseudoinverse, Algorithm

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