An efficient algorithm for solving absolute value equations

A. Fakharzadeh, N. Naseri Shams


Recently, absolute value equations (AVEs) are lied in theconsideration center of some researchers since they are very suitable al-ternatives for many frequently occurring optimization problems. There-fore, nding a fast solution method for these type of problems is verysignicant. In this paper, based on the mixed-type splitting (MTS) ideafor solving linear system of equations, a new fast algorithm for solvingAVEs is presented. This algorithm has two auxiliary matrices whichare limited to be nonnegative strictly lower triangular and nonnega-tive diagonal matrices. The convergence of the algorithm is discussedvia some theorems. In addition, it is shown that by suitable choice ofthe auxiliary matrices, the convergence rate of this algorithm is fasterthan that of the SOR, AOR, Generalized Newton, Picard and SOR-like methods. Eventually, some numerical results for dierent size ofproblem dimensionality are presented which admit the credibility of theproposed algorithm.


Absolute value equations, M−splitting, Mixed-type splitting method, Unique solution, Spectral radius.

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