一种实用的线性方程组迭代预处理算法

A Practical Preconditioning Algorithm of Iteration for Linear Systems

针对传统解线性方程组Ax=b的迭代法的局限性,通过引入全主元矩阵的概念,提出了一种改进算法,先将线性方程组的系数矩阵A变换成全主元矩阵,然后再进行迭代。数值实验结果表明:该算法可大大提高迭代法的收敛比率。

There exists limitation in the traditional iteration methods of solving linear systems Ax = b. This paper introduces the concept of whole - main - factor - matrix, proposes a kind of new preconditioning algorithm, translates the coefficient matrix of linear systems into whole - main - factor - matrix and then introduces the methods of iteration. Numerical experiments show that the algorithm can improve the rate of convergence effectively.