Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 126908, 6 pages
http://dx.doi.org/10.5402/2012/126908
Research Article

A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem

1College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 14 September 2011; Accepted 3 October 2011

Academic Editors: T. Allahviranloo and K. Eom

Copyright Β© 2012 Xuefeng Duan and Chunmei Li. 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

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations 𝐴𝑋𝐡=𝐸, 𝐢𝑋𝐷=𝐹, which arises frequently in experimental design. If we choose the initial iterative matrix 𝑋0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.