求解特征值互补问题的一类ABS算法

An ABS Algorithm for Eigenvalue Complementarity Problem

ABS算法是20世纪80年代初,由Abaffy,Broyden和Spedicato完成的用于求解线性方程组的含有三个参量的投影算法,是一类有限次迭代直接法。目前,ABS算法不仅可以求解线性与非线性方程组,还可以求解线性规划和具有线性约束的非线性规划等问题。本文即是利用ABS算法求解特征值互补问题的一种尝试,构造了求解特征值互补问题的ABS算法,证明了求解特征值互补问题的ABS算法的收敛性。数值例子充分验证了求解特征值互补问题的ABS算法的有效性。

An ABS algorithm is a projection algorithm with three parameters for solving linear equations, constructed by Abaffy, Broyden and Spedicato in the early 1980s. It is a kind of finite iterative direct method. At present, the ABS algorithm can solve not only the linear and nonlinear equations, but the linear programming and nonlinear programming problems with linear constraints as well. This paper is an attempt to solve the eigenvalue complementarity problem by ABS algorithm. The ABS algorithm for solving the eigenvalue complementarity problem is constructed and the convergence of the algorithm is proved. Numerical examples are presented to indicate the effectiveness of the algorithm.