Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 301971, 7 pages
http://dx.doi.org/10.1155/2012/301971
Research Article

A Fast Algorithm of Moore-Penrose Inverse for the Loewner-Type Matrix

QiuJuan Tong,1,2 SanYang Liu,1 and Quan Lu3

1School of Science, Xidian University, Xi'an 710071, China
2School of Science, Xi'an University of Post and Telecommunications, Xi'an 710061, China
3Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received 25 July 2011; Accepted 8 October 2011

Academic Editor: Tadeusz Kaczorek

Copyright © 2012 QiuJuan Tong et al. 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

In this paper, we present a fast algorithm of Moore-Penrose inverse for m×n Loewner-type matrix with full column rank by forming a special block matrix and studying its inverse. Its computation complexity is O(mn)+O(n2), but it is O(mn2)+O(n3) by using L+=(LTL)−1LT.