Abstract:
We present a little-known 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 two classes of existing preconditioners: modified incomplete-Cholesky and multilevel diagonal scaling. The paper also contains a presentation of Vaidya's preconditioners, which was previously missing from the literature.