Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 27, Issue 4, Pages 930-951Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0895479801384019
Keywords
support preconditioners; combinatorial preconditioners; support theory; support-tree preconditioners; modified incomplete factorizations
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We present a preconditioning technique, called support-graph preconditioning, and use it to analyze two classes of preconditioners. The technique was first described in a talk by Pravin Vaidya, who did not formally publish his results. Vaidya used the technique to devise and analyze a class of novel preconditioners. The technique was later extended by Gremban and Miller, who used it in the development and analysis of yet another class of new preconditioners. This paper extends the technique further and uses it to analyze a class of existing preconditioners, modified incomplete Cholesky. The paper also contains a presentation of Vaidya's preconditioners, which was previously missing from the literature.
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