SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Conditioning of incomplete Cholesky factorizations with orthogonal approximations

A. Napov

Abstract
We consider incomplete Cholesky factorizations based on orthogonal approximations for the iterative solution of symmetric positive definite linear systems. Such factorizations correspond, for instance, to some existing fast direct solvers based on low-rank approximations and which are used with large approximation threshold. Large threshold enables a cheaper factorization, but the resulting solution is less accurate and additional solution steps may be required to refine it, yielding an iterative solver. The number of iterations then depends on the condition number of the preconditioned system, and we show that this latter may be bounded depending only on the accuracy of the individual approximations. The resulting bound is illustrated with some existing factorization algorithms in the context of discretized elliptic partial differential equations.

Bibliography
[1] A. Napov, Conditioning analysis of incomplete Cholesky factorizations with orthogonal dropping, SIAM J. Matrix Anal. Appl. (to appear)

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