Analysis of acceleration strategies for restarted minimal residual methods
Analysis of acceleration strategies for restarted minimal residual methods
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DOI：
10.1016/s0377-0427(00)00398-8
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发表时间：
2000-11
影响因子：
2.4
通讯作者：
M. Eiermann;O. Ernst;O. Schneider
中科院分区：
文献类型：
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作者：
M. Eiermann;O. Ernst;O. Schneider
我们提供了一个概述，现有的战略，弥补最小残差（MR）Krylov子空间方法的收敛性恶化，由于重新启动。我们评估流行的做法，使用几乎不变的子空间，以增加Krylov子空间或构造预条件，这些子空间反转。在这些空间是完全不变的情况下，增强方法被证明是上级。我们进一步展示了如何最近推出的战略de Sturler截断近似空间的MR方法可以被解释为一个控制松动的条件下，全球MR近似的子空间之间的典型角度的基础上。对于Krylov子空间方法的特殊情况下，我们给出了一个简洁的推导过程中的作用的Ritz和调和Ritz值和向量的多项式描述Krylov空间以及使用隐式更新Arnoldi方法操纵Krylov空间。
We provide an overview of existing strategies which compensate for the deterioration of convergence of minimum residual (MR) Krylov subspace methods due to restarting. We evaluate the popular practice of using nearly invariant subspaces to either augment Krylov subspaces or to construct preconditioners which invert on these subspaces. In the case where these spaces are exactly invariant, the augmentation approach is shown to be superior. We further show how a strategy recently introduced by de Sturler for truncating the approximation space of an MR method can be interpreted as a controlled loosening of the condition for global MR approximation based on the canonical angles between subspaces. For the special case of Krylov subspace methods, we give a concise derivation of the role of Ritz and harmonic Ritz values and vectors in the polynomial description of Krylov spaces as well as of the use of the implicitly updated Arnoldi method for manipulating Krylov spaces.