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Solving symmetric indefinite systems using memory efficient incomplete factorization preconditioners
J Scott (STFC Rutherford Appleton Lab.)
Sparse symmetric indefinite linear systems of equations arise in numerous practical applications. In many situations, an iterative method is the method of choice but a preconditioner is normally required for this to be effective. In this paper, the focus is on the development of incomplete factorization algorithms that can be used to compute high quality preconditioners for general indfinite systems, including saddle-point problems. A limited memory approach is used that generalises recent work on incomplete Cholesky factorization preconditioners. A number of new ideas are proposed with the goal of improving the stability, robustness and efficiency of the resulting preconditioner. These include the monitoring of stability as the factorization proceeds and the use of pivot modifications when potential instability is observed. Numerical experiments involving test problems arising from a range of real-world applications are used to demonstrate the effectiveness of our approach and comparisons are made with a state-of-the-art sparse direct solver.
SIAM J Sci Comput
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