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Lower bounds for graph embeddings and combinatorial preconditioners
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Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Algebraic analysis of high-pass quantization
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Some preconditioning techniques for linear systems
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ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Computer Vision and Image Understanding
Spectral Sparsification of Graphs
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Power grid analysis with hierarchical support graphs
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The laplacian paradigm: emerging algorithms for massive graphs
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Algorithms, graph theory, and the solution of laplacian linear equations
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Proceedings of the International Conference on Computer-Aided Design
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Proceedings of the International Conference on Computer-Aided Design
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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.