求解大型非对称线性方程组的灵活的Minpert算法

The Flexible Minpert Algorithm for Large Unsymmetric Linear Systems

对于病态的线性方程组,数值求解必须小心进行,为了加快算法的收敛速度,一种有效的方法是对原方程组作某些预处理.Kasenally和Simoncini给出了求解大型非对称线性方程组的最小联合向后扰动方法(Minpert算法).为了加快Minpert的收敛速度,我们结合右预处理技术,提出了收敛效果非常好的灵活的Minpert算法,即FMin-pert算法.数值例子表明FMinpert的收敛速度确实比Minpert快了很多,且有时收敛得比FGMRES更好.

Kasenally and Simoncini posed the Minpert method for large unsymmetric linear systems. In order to accelerate the convergence rate of the Minpert algorithm, we use right preconditioning technique, and present the flexible Minpert （FMinpert） in this paper. Numerical experiments show the new method can achieve good convergence rate and sometimes has better performance than the restarted FGMRES method.