Lecture notes from IPCO Summer School 2005 Fast Randomized Algorithms for Partitioning, Sparsification, and Solving Linear Systems

4 Combinatorial Preconditioners 6 4.1 Graphic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Graphic Inequalities with Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.3 Augmented Tree Preconditioners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.4 Sparsifying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.5 Proving sparsifiers exist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.6 History of Combinatorial Preconditioning . . . . . . . . . . . . . . . . . . . . . . . . 13

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