On the iterative methods for weighted linear least squares problem

Abstract

Purpose The Weighted Linear Least Squares (WLLS) problem has many different applications in sciences and engineering. The purpose of this paper is to introduce an iterative scheme for solving the WLLS problem. Design/methodology/approach By considering the splitting techniques in conjunction with Generalized Accelerated Over-relaxation (GAOR) method the authors design a new iterative method to solve the weighted linear least squares problem. Furthermore, within the computational framework, some models of iterative schemes candidates are investigated and evaluated. Findings In this paper, the authors propose an efficient iterative scheme for solving the WLLS problem. The proposed scheme presented promising results from the aspects of both convergence behavior and performance. Moreover, comparative results for the proposed schemes are also presented. Research limitations/implications Comparison between the new methods and other similar methods for the studied problem shows a remarkable agreement and reveals that the new model is much better in comparison with the existing methods in point of view rate of convergence and computing efficiency, as illustrated by the theoretical analysis and numerical results presented. Originality/value For solving WLLS more attention has recently been paid on a special class of splitting techniques with the preconditioned GAOR method. In this paper, the authors use a different splitting for the GAOR method and present a promising class of methods. The convergence results of the iterative algorithm are also proposed. Several examples are given to show the efficiency of the presented methods.