用修改的Lanczos方法解大型稀疏线性方程组

SOME VARIANTS OF LANCZOS METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS

引言 解大型稀疏线性方程组Ax=b,已有许多方法,但这些方法基本上是针对对称正定矩阵或非零元分布较有规律的矩阵。对于一般的特大型稀疏矩阵的有效解法还在寻找过程中,其中一个途径是从Lanczos方法入手,采取各种变形。 我们受Paige和Saunders的算法SYMMLQ的启发。

Inspired by the algorithm of Paige and Saunders, we suggest two algorithms forsolving large sparse unsymmetric linear systems. They are equivalent to the biconju-gate gradient method in theory, but better in numerical stability.