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首页> 外文期刊>American Journal of Computational and Applied Mathematics >Stopping Criteria of the Extended Iterative Refinement Algorithm Used to Solve an Ill Conditioned Linear System
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Stopping Criteria of the Extended Iterative Refinement Algorithm Used to Solve an Ill Conditioned Linear System

机译：解病态线性系统的扩展迭代细化算法的停止准则

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摘要

We proved in[1] that our extended iterative refinement or improvement algorithm to solve accurately an ill conditioned linear system converges by providing a theorem that we called the convergence theorem. To compute an accurate solution to an ill conditioned linear system we first use the additive preconditioning to decrease the condition number of the input ill conditioned matrix . Then we use the technique of Schur aggregation to reduce the computation of to the computation of the Schur aggregate . This second step is done using the Sherman-Morrison-Woodbury (SMW) formula. The extended iterative refinement or improvement algorithm should stop when and the Schur aggregate are computed with higher precision. We provide in this paper the condition for the extended iterative refinement or improvement algorithm to stop in a proposition.
机译：我们在[1]中证明了通过提供一个称为收敛定理的定理，我们的扩展迭代细化或改进算法可以精确求解病态线性系统，从而收敛。为了计算病态线性系统的精确解，我们首先使用加性预处理来减少输入病态矩阵的条件数。然后利用Schur聚合技术将的计算简化为Schur聚合的计算。第二步是使用Sherman-Morrison-Woodbury（SMW）公式完成的。当以较高的精度计算Schur集合和Schur集合时，扩展的迭代细化或改进算法应停止。我们在本文中提供了扩展的迭代细化或改进算法停止在命题中的条件。

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