Error Estimation in Preconditioned Conjugate Gradients
Error Estimation in Preconditioned Conjugate Gradients
复制标题
预条件共轭梯度中的误差估计
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Petr Tichý
中科院分区：
文献类型：
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作者：
Z. Strakoš;Petr Tichý
在实际问题中，迭代方法很难在没有收敛加速的情况下使用，这通常被称为预条件，这通常是通过将一些(不完整或修改的)直接算法作为迭代的一部分来实现的。当达到期望的精度时，随着停止迭代的可能性，预条件迭代方法的有效性增加。然而，这需要将获得的精度的适当测量作为计算的一部分。本文的目标是描述一种简单且在数值上可靠的预条件共轭梯度法误差大小的估计。通过这种方式，本文推广了[Z.Strakoš和P.Tich Axi，Etna，13(2002年)，pp.56-80]的结果，并将它们传达给预条件共轭梯度法的实际用户。
In practical problems, iterative methods can hardly be used without some acceleration of convergence, commonly called preconditioning, which is typically achieved by incorporation of some (incomplete or modified) direct algorithm as a part of the iteration. Effectiveness of preconditioned iterative methods increases with possibility of stopping the iteration when the desired accuracy is reached. This requires, however, incorporating a proper measure of achieved accuracy as a part of computation.The goal of this paper is to describe a simple and numerically reliable estimation of the size of the error in the preconditioned conjugate gradient method. In this way this paper extends results from [Z. Strakoš and P. Tichý, ETNA, 13 (2002), pp. 56–80] and communicates them to practical users of the preconditioned conjugate gradient method.