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arXiv · 2412.12608

SOR-like iteration and FPI are consistent when they are equipped with certain optimal iterative parameters

Jiayu Liu·Tingting Luo·Cairong Chen·Deren Han
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Abstract

Two common methods for solving absolute value equations (AVE) are SOR-like iteration method and fixed point iteration (FPI) method. In this paper, novel convergence analysis, which result wider convergence range, of the SOR-like iteration and the FPI are given. Based on the new analysis, a new optimal iterative parameter with a analytical form is obtained for the SOR-like iteration. In addition, an optimal iterative parameter with a analytical form is also obtained for FPI. Surprisingly, the SOR-like iteration and the FPI are the same whenever they are equipped with our optimal iterative parameters. As a by product, we give two new constructive proof for a well known sufficient condition such that AVE has a unique solution for any right hand side. Numerical results demonstrate our claims.

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Jiayu Liu, Tingting Luo, Cairong Chen, Deren Han. 2024-12-17. SOR-like iteration and FPI are consistent when they are equipped with certain optimal iterative parameters. https://arxiv.org/abs/2412.12608

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