On the SOR-like iteration method for solving absolute value equations

Abstract In this paper, we further consider the SOR-like iteration method for solving absolute value equations. Some new convergence conditions are obtained from the involved iteration matrix of the SOR-like iteration method, which are different from the results by Ke and Ma (2017). Numerical experiments show that the SOR-like iteration method for solving absolute value equations is efficient and feasible.

[1]  Davod Khojasteh Salkuyeh,et al.  The Picard–HSS iteration method for absolute value equations , 2014, Optim. Lett..

[2]  Gene H. Golub,et al.  SOR-like Methods for Augmented Systems , 2001 .

[3]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[4]  Cui-Xia Li,et al.  The unique solution of the absolute value equations , 2018, Appl. Math. Lett..

[5]  O. Mangasarian,et al.  Absolute value equations , 2006 .

[6]  Olvi L. Mangasarian,et al.  Absolute value programming , 2007, Comput. Optim. Appl..

[7]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[8]  Changfeng Ma,et al.  SOR-like iteration method for solving absolute value equations , 2017, Appl. Math. Comput..

[9]  Cui-Xia Li,et al.  A Preconditioned AOR Iterative Method for the Absolute Value Equations , 2017 .

[10]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[11]  Jiri Rohn,et al.  A theorem of the alternatives for the equation |Ax| − |B||x| = b , 2004, Optimization Letters.

[12]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[13]  Cui-Xia Li,et al.  A Modified Generalized Newton Method for Absolute Value Equations , 2016, J. Optim. Theory Appl..

[14]  Olvi L. Mangasarian,et al.  A generalized Newton method for absolute value equations , 2009, Optim. Lett..

[15]  Davod Khojasteh Salkuyeh,et al.  A generalization of the Gauss-Seidel iteration method for solving absolute value equations , 2017, Appl. Math. Comput..