Research Article
A Modified Gauss-Seidel Iteration Method for Solving Absolute Value Equations
@INPROCEEDINGS{10.1007/978-3-030-72792-5_13, author={Peng Guo and Shi-liang Wu}, title={A Modified Gauss-Seidel Iteration Method for Solving Absolute Value Equations}, proceedings={Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part I}, proceedings_a={SIMUTOOLS}, year={2021}, month={4}, keywords={Absolute value equation Gauss-Seidel splitting MGS iteration method Convergence theory}, doi={10.1007/978-3-030-72792-5_13} }- Peng Guo
Shi-liang Wu
Year: 2021
A Modified Gauss-Seidel Iteration Method for Solving Absolute Value Equations
SIMUTOOLS
Springer
DOI: 10.1007/978-3-030-72792-5_13
Abstract
The iterative Gauss-Seidel method is an effective and practical method for solving the absolute value equations. However, the solution efficiency of this method usually decreases, and even the equation cannot be solved even when the problem reaches a certain large scale. To improve the efficiency of the Gauss-Seidel method for solving absolute value equations, a modified Gauss-Seidel (MGS) iteration method is presented in this paper. In the our method, we create a diagonal matrix(\varOmega )with nonnegative diagonal elements in the Gauss-Seidel matrix splitting. Under the given constraints the convergence theory of the MGS method have been studied. The numerical results show that the method is effective. It can be noted that with the increase in the scale of the problem, the setting effect of the matrix(\varOmega )is more obvious.
