Comments on the GMRES Convergence for Preconditioned Systems
Comments on the GMRES Convergence for Preconditioned Systems
复制标题
对预处理系统 GMRES 收敛的评论
DOI：
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复制
发表时间：
2009
期刊：
影响因子：
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通讯作者：
B. Philippe
中科院分区：
文献类型：
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作者：
N. Gmati;B. Philippe
本文的目的是评论工程师研究声散射的一个频繁的观察。它与GMRES方法在求解方程组Ax= b，其中A= Ii，？B。本文包括一个定理，表示收敛速度时，一些特征值的Bhave模大于1，该速度取决于速度测量时，解决系统的谱投影到不变的子空间对应的其他特征值。定理的结论在Helmholtz方程上得到了证明。
The purpose of this paper is to comment a frequent observation by the engineers studying acoustic scattering. It is related to the convergence of the GMRES method when solving systems Ax= bwith A= Ii¾? B. The paper includes a theorem which expresses the convergence rate when some eigenvalues of Bhave modulus larger than one; that rate depends on the rate measured when solving the system obtained by spectral projection onto the invariant subspace corresponding to the other eigenvalues. The conclusion of the theorem is illustrated on the Helmholtz equation.