极大熵Newton-SOR迭代算法求解绝对值方程

Solving absolute value equation based on maximum entropy Newton-SOR algorithm

主要研究绝对值方程Ax+B|x|=b的求解问题.首先通过利用极大熵理论将该绝对值方程转化为光滑方程组,建立求解该形式绝对值问题的Newton-SOR方法,并对算法的收敛性进行分析和证明;最后通过数值试验对算法的有效性进行测试.

This paper is concerned with the absolute value equation Ax ＋ B ｜ x ｜ = b. First, using the maximum entropy function, and absolute value equations problem could be transformed into the approximation unconstrained differentiable problem, then using the Newton -SOR method to solve this problem. Theoretic analysis shows that the proposed method is effective. Numerical results indicate that the method is feasible and effective to absolute value equations problem.