A survey of subspace recycling iterative methods
A survey of subspace recycling iterative methods
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DOI：
10.1002/gamm.202000016
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Kirk M. Soodhalter;E. D. Sturler;M. Kilmer
中科院分区：
文献类型：
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作者：
Kirk M. Soodhalter;E. D. Sturler;M. Kilmer
本综述涉及子空间循环方法，这是一类流行的迭代方法，可以有效地重用子空间信息，以加快收敛速度，并在具有缓慢变化的系数矩阵、多个右侧或两者的线性系统序列上找到良好的初始向量。被再循环的子空间信息通常在一个或多个系统上运行迭代方法（通常是Krylov子空间方法）期间生成。在介绍了定义和符号之后，我们研究了早期增强方案的历史，沿着的是紧缩预处理方案，以及它们对回收方法发展的影响。然后，我们讨论了一个一般的剩余约束框架，通过它可以看到许多增强Krylov和回收方法。在此框架内，我们回顾了几种增强和回收方法。然后，我们讨论了一些已知的有效策略，选择子空间进行回收，然后带读者通过最近的发展，这些发展已经推广了移位线性系统（序列）的回收，其中一些考虑了多个右侧。我们圆了我们的调查，已经看到受益于子空间回收方法的应用领域的简要回顾。
This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial vectors over a sequence of linear systems with slowly changing coefficient matrices, multiple right‐hand sides, or both. The subspace information that is recycled is usually generated during the run of an iterative method (usually a Krylov subspace method) on one or more of the systems. Following introduction of definitions and notation, we examine the history of early augmentation schemes along with deflation preconditioning schemes and their influence on the development of recycling methods. We then discuss a general residual constraint framework through which many augmented Krylov and recycling methods can both be viewed. We review several augmented and recycling methods within this framework. We then discuss some known effective strategies for choosing subspaces to recycle before taking the reader through more recent developments that have generalized recycling for (sequences of) shifted linear systems, some of them with multiple right‐hand sides in mind. We round out our survey with a brief review of application areas that have seen benefit from subspace recycling methods.