Iterative Regularization and MINRES
Iterative Regularization and MINRES
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DOI：
10.1137/s0895479898348623
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发表时间：
1999-10
期刊：
影响因子：
--
通讯作者：
M. Kilmer;G. Stewart
中科院分区：
文献类型：
--
作者：
M. Kilmer;G. Stewart
在本文中，我们提出了三个定理，使洞察到正规化性质的MINRES。虽然我们的理论没有完全描述算法的正则化行为，但它提供了对该方法观察到的行为的部分解释。与传统的试图解释的Krylov子空间方法的正则化性能，我们的方法侧重于收敛性能的残差，而不是对谐波里兹值的收敛性分析。我们的分析的进口说明了两个例子。特别是，我们的理论和数值结果支持以下重要的观察：在某些情况下，最佳Krylov子空间的维度可以远远小于截断谱的解决方案，必须计算，以达到可比的精度的组件的数量。
In this paper we present three theorems which give insight into the regularizing properties of MINRES. While our theory does not completely characterize the regularizing behavior of the algorithm, it provides a partial explanation of the observed behavior of the method. Unlike traditional attempts to explain the regularizing properties of Krylov subspace methods, our approach focuses on convergence properties of the residual rather than on convergence analysis of the harmonic Ritz values. The import of our analysis is illustrated by two examples. In particular, our theoretical and numerical results support the following important observation: in some circumstances the dimension of the optimal Krylov subspace can be much smaller than the number of the components of the truncated spectral solution that must be computed to attain comparable accuracy.