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Unformatted text preview: CS 290N/219: Sparse matrix algorithms: Homework 3 Assigned October 19, 2009 Due by class Wednesday, October 28 1. [20 points] Let G be the graph of the n-vertex model problem, that is, a k-by- k grid graph with n = k 2 vertices. Prove that there is some constant c > 0 such that for every elimination ordering on G , the filled graph G + contains a complete subgraph with at least c n vertices. (A complete subgraph is a set of vertices such that every pair is joined by an edge.) Hint: Suppose youre given an ordering for the vertices of G . Think of playing the graph game in the given order, and consider the first time that youve either marked all the vertices in any single row of the entire grid or else marked all the vertices in any single column. 2. [40 points] (see Davis problem 6.13). An incomplete LU factorization is an approximate factorization A LU , in which L and U are lower and upper triangular matrices whose product is approximately A in some sense, but L and...
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This note was uploaded on 12/27/2011 for the course CMPSC 290h taught by Professor Chong during the Fall '09 term at UCSB.
- Fall '09