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Mathematical Problems in Engineering
Volume 2016, Article ID 9065438, 16 pages
http://dx.doi.org/10.1155/2016/9065438
Research Article

Computing the Pseudoinverse of Specific Toeplitz Matrices Using Rank-One Updates

1University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia
2Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
3Faculty of Computer Science, Goce Delčev University, Goce Delčev 89, 2000 Štip, Macedonia

Received 29 February 2016; Accepted 3 July 2016

Academic Editor: Masoud Hajarian

Copyright © 2016 Predrag S. Stanimirović 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

Application of the pure rank-one update algorithm as well as a combination of rank-one updates and the Sherman-Morrison formula in computing the Moore-Penrose inverse of the particular Toeplitz matrix is investigated in the present paper. Such Toeplitz matrices appear in the image restoration process and in many scientific areas that use the convolution. Four different approaches are developed, implemented, and tested on a number of numerical experiments.