Preconditioners for Krylov subspace methods: An overview
Preconditioners for Krylov subspace methods: An overview
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DOI：
10.1002/gamm.202000015
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
J. Pearson;J. Pestana
中科院分区：
文献类型：
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作者：
J. Pearson;J. Pestana
在模拟科学或工程或工业过程的机制时，经常需要构建数学模型，然后用数值方法求解该模型。如果精确的数值解是必要的或可取的，这可能涉及求解大规模方程组。一类主要的求解方法是预处理迭代法，涉及计算成本低的预处理器，同时还捕获包含在线性系统中的信息。在这篇文章中，我们给出了一个简短的调查领域的预处理。我们介绍了一系列的预处理偏微分方程，其次是优化问题，在讨论预处理构造少标准目标铭记。
When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large‐scale systems of equations. One major class of solution methods is that of preconditioned iterative methods, involving preconditioners which are computationally cheap to apply while also capturing information contained in the linear system. In this article, we give a short survey of the field of preconditioning. We introduce a range of preconditioners for partial differential equations, followed by optimization problems, before discussing preconditioners constructed with less standard objectives in mind.