Abstract
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.
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AMS subject classification (2000)
15A06, 65F10, 65F25, 65G50
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Strakoš, Z., Tichý, P. Error Estimation in Preconditioned Conjugate Gradients. Bit Numer Math 45, 789–817 (2005). https://doi.org/10.1007/s10543-005-0032-1
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DOI: https://doi.org/10.1007/s10543-005-0032-1