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Persistent URL http://purl.org/net/epubs/work/65828
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Record Id 65828
Title Projected Krylov methods for general saddle-point systems
Abstract Suppose we wish to solve Ax = b, where A is saddle point matrix. A popular method of speeding up convergence of a Krylov subspace method applied to a A is to employ a constraint preconditioner -- i.e. a matrix P where the (1,1) block of A, H, is replaced by some approximation G. In the case where both H and G are symmetric positive definite on the null-space of B, Gould, Hribar and Nocedal showed that a constraint preconditioner can be applied via a projected conjugate gradient method. Although this method acts on matrices in the full space, it is equivalent to solving an equation with the reduced system Z^T A Z using a preconditioner Z^T G Z, where Z is a null matrix of B. In this talk I will describe how, via a set of systematic principles, the projected approach can be made to work for all Krylov subspace algorithms based on an Arnoldi or bi-Lanczos procedure, not only conjugate gradients. One consequence of this is that certain well known methods -- e.g. MINRES -- are, under certain circumstances, well definned in the presence of an indefinite preconditioner.
Organisation STFC , SCI-COMP , SCI-COMP-CM
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Language English (EN)
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Presentation Presented at International Conference On Preconditioning Techniques For Scientific And Industrial Applications, Oxford, UK, 19-21 Jun 2013. Oxford2013.pdf 2013