MINBACK:解对称线性方程组的极小化向后误差方法

Minback: A Minimum Backward Error Algorithm For Symmetric Linear Systems

本文提出了求解对称线性方程组bAx=的一个方法—— MINBACK方法。该方法利用Lanczos过程产生Krylov 子空间),(0rAkm的一组基,并求近似解),(00rAkxxmm+使系数矩阵A的向后误差范数minFD最小化。本文给出了Lanczos方法和MINRES 方法的全体向后误差的集合的通式,分析了算法的性质,讨论了算法的执行,最后,给出了结论。

MINBACK method as an analytical for symmetric linear systems was given in this paper. The method computes ),(00rAkxxmm+ and minimizes the norm of backward error. The set of all backward error of Lanczos method and MINRES method were presented. We derived the minimal norm minFD. And gave the result simultaneously.