Two new fixed point iterative schemes for absolute value equations

摘要

Abstract Absolute value equations (AVEs) can be used to solve many engineering, management science, and operations research problems. This paper proposes two new iterative schemes for solving Ax-|x|=bdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Ax-{|x|}= b$$end{document}, where A is an M-matrix. These methods depend on the splitting of the coefficient matrix. The convergence conditions for these two methods are given. Some numerical examples are given to demonstrate that the iterative schemes are valid and efficient. The results are inspiring and may animate more study in this direction.