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Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners
Author(s) -
Scott Jennifer,
Tůma Miroslav
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2099
Subject(s) - preconditioner , robustness (evolution) , factorization , incomplete lu factorization , incomplete cholesky factorization , mathematics , linear system , stability (learning theory) , iterative method , numerical stability , mathematical optimization , algorithm , computer science , numerical analysis , sparse matrix , matrix decomposition , mathematical analysis , machine learning , biochemistry , chemistry , eigenvalues and eigenvectors , physics , quantum mechanics , gaussian , gene
Summary 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.