Abstract and Applied Analysis
Volume 2012 (2012), Article ID 406232, 9 pages
http://dx.doi.org/10.1155/2012/406232
Research Article

Residual Iterative Method for Solving Absolute Value Equations

Muhammad Aslam Noor,1 Javed Iqbal,1 and Eisa Al-Said2

1Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan
2Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia

Received 30 November 2011; Accepted 13 December 2011

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Muhammad Aslam Noor 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

We suggest and analyze a residual iterative method for solving absolute value equations 𝐴 𝑥 − | 𝑥 | = 𝑏 where 𝐴 ∈ 𝑅 𝑛 × 𝑛 , 𝑏 ∈ 𝑅 𝑛 are given and 𝑥 ∈ 𝑅 𝑛 is unknown, using the projection technique. We also discuss the convergence of the proposed method. Several examples are given to illustrate the implementation and efficiency of the method. Comparison with other methods is also given. Results proved in this paper may stimulate further research in this fascinating field.