WGMRES method of simple deformation

Abstract

Abstract: The GMRES method is a popular iterative method for the solution of equation with a large nonsymmetric nonsingular matrix. There are some algorithms of improvement in the calculation. Weighted GMRES uses the weighted methods to accelerate the speed of convergence. The calculation process of WGMRES algorithm is introduced, then a simple deformation is made to the calculation process, and it puts forward a new calculation method. The experimental results demonstrate the method has higher convergence.

Key words: Weighted GMRES, Krylov subspace, Givens rotations, iterative method

摘要： GMRES方法是解决大型稀疏非对称的线性方程组最有效的方法，在计算中存在着许多对标准GMRES进行改进的算法。Weighted GMRES算法使用加权方式来加快GMRES算法的收敛速度。主要研究WGMRES算法的计算过程，并对此做出简单的变形，从而提出一种新的计算方法。实验结果表明，该方法具有加快收敛的效果。

关键词: Weighted GMRES算法, Krylov子空间, Givens变换, 迭代方法

DING Bolun, CHEN Guangxi. WGMRES method of simple deformation[J]. Computer Engineering and Applications, 2013, 49(13): 48-50.

丁伯伦，陈光喜. 一种微变形的WGMRES算法[J]. 计算机工程与应用, 2013, 49(13): 48-50.

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WGMRES method of simple deformation

一种微变形的WGMRES算法

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