采用高阶近似逆矩阵的块PCG法

A BLOCK PRECONDITIONED CONJUGATE GRADIENT METHOD USING HIGH ORDER APPROXIMATE INVERSES

本文应用矩阵元素阶、阶矩阵及消去法的影响域等概念,给出了强主元多对角阵高阶近似求逆的一种快速算法。在强主元条件下,该法可应用于非对称阵和非正定阵。本文将该法与块预处理共轭梯度法相结合,应用于椭圆型方程数值解及类似问题的计算。数值结果表明,该法不仅适用范围较广,也具有较高的计算效率。

A fast method is presented to compute high order approximate inverses for multidiagonal banded matrices of strong pivot. It is based on several concepts such as the order of an element in a strong pivot matrix, the order matrix and the influence areas of elimination steps.Under the condition of strong pivot, this method can be applied to unsymmetric and indefinite matrices. Coupling with the block preconditioned conjugate gradient, it is used for the numerical solution of elliptic partial differential equations and similar problems. It is demonstrated by the computational experiments that the method reported here has a higher efficiency in computations , comparing with similar methods.