一种加权块simpler GMRES算法及应用

A Weighted Block Simpler GMRES Algorithm and Its Applications

【目的】为了更加稳定地快速求解非对称多右端项线性方程组,解决实际应用问题。【方法】有效利用加权策略和分析基底条件数,对块simpler GMRES方法进行了改进。【结果】提出加权块simpler GMRES算法,并对算法的数值稳定性进行分析,得出初始块残量的单位化是新算法数值稳定的关键,以及加权矩阵的一个不变性质。【结论】数值算例表明新算法具有良好的稳定性,能快速稳定地求解目标方程组。

[Purposes]To solve the linear equations of asymmetric multiple right-end terms more quickly and stably.[Methods]Effective weighted strategy and the analysis for the basis condition number are used to improve the block simpler GMRES method.[Findings]The weighted block simpler GMRES algorithm is proposed,and the numerical stability analysis of the algorithm is carried out.It is concluded that the unitization of the initial block residual is the key to the numerical stability of the new algorithm.And there also gets an invariant property of the weighted matrix.[Conclusions]Numerical examples show that the new algorithm has good stability and can solve the target equations faster.