GMRES Convergence for Perturbed Coefficient Matrices, with Application to Approximate Deflation Preconditioning
GMRES Convergence for Perturbed Coefficient Matrices, with Application to Approximate Deflation Preconditioning
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DOI：
10.1137/120884328
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发表时间：
2013-07
期刊：
影响因子：
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通讯作者：
Josef A. Sifuentes;M. Embree;R. Morgan
中科院分区：
文献类型：
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作者：
Josef A. Sifuentes;M. Embree;R. Morgan
当系数矩阵扰动时，GMRES收敛性如何变化？使用谱扰动理论和预解估计，我们开发了简单的，一般的界限，量化的滞后收敛这样的扰动可以诱导。这种分析特别适用于预处理系统，其中理想的预处理器仅近似应用于实际计算。为了说明这种方法的实用性，我们结合联合收割机我们的分析与Stewart的不变子空间扰动理论，开发严格的边界上的性能近似紧缩预处理使用里兹向量。
How does GMRES convergence change when the coefficient matrix is perturbed? Using spectral perturbation theory and resolvent estimates, we develop simple, general bounds that quantify the lag in convergence such a perturbation can induce. This analysis is particularly relevant to preconditioned systems, where an ideal preconditioner is only approximately applied in practical computations. To illustrate the utility of this approach, we combine our analysis with Stewart's invariant subspace perturbation theory to develop rigorous bounds on the performance of approximate deflation preconditioning using Ritz vectors.