Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners |
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Authors: | Jennifer Scott Miroslav Tůma |
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Institution: | 1. Scientific Computing Department, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK;2. Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic;3. Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic |
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Abstract: | 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 it to be effective. In this paper, the focus is on a class of incomplete factorization algorithms that can be used to compute preconditioners for symmetric indefinite systems. A limited memory approach is employed that incorporates a number of new ideas with the goal of improving the stability, robustness, and efficiency of the preconditioner. These include the monitoring of stability as the factorization proceeds and the incorporation of pivot modifications when potential instability is observed. Numerical experiments involving test problems arising from a range of real‐world applications demonstrate the effectiveness of our approach. |
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Keywords: | incomplete factorizations indefinite symmetric systems iterative solvers pivoting preconditioning sparse linear systems sparse matrices |
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