求解线性互补问题的改进加速迭代方法

Modified Accelerated Splitting Iteration Method for Linear Complementarity Problem

从基于模系数矩阵分裂迭代方法的演变方法出发,将收敛所需满足的条件一般化,提出了一种改进的加速分裂迭代方法.理论分析表明新方法可以和线性互补问题等价转换,将新方法与其他几种方法进行比较分析,给出了系数矩阵是H+-矩阵的收敛定理.最后,通过数值算例证明了提出的新方法在运算过程中需要更少的迭代步数和更短的运行时间.

Based on evolution method of modulus-based matrix splitting iteration method, the convergence condition was generalized;a modified accelerated splitting iteration method was proposed.The new method can be proved to be equivalent to the linear complementarity problem theoretically and compared to other methods;a new convergence theorem with matrix was put forward.With numerical examples,the new method was proved to need less iteration step numbers and shorter running time.