Administrivia : October 12, 2009. No class this Wednesday, October 14 Homework 2 due Wednesday in HFH homework boxes (mail room next to CS office on second floor) Reading in Davis: Section 7.1 (min degree – you can skim the details) Sections 7.2 – 7.4 (nonsymmetric permutations).
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5Graphs and Sparse Matrices: Cholesky factorization
Fill:new nonzeros in factor
Symmetric Gaussian elimination:
for j = 1 to n add edges between j’s higher-numbered neighbors
Let G = G(A) be the graph of a symmetric, positive definite matrix, with vertices 1, 2, …, n, and let G+ = G+(A)be the filled graph.
Then (v, w) is an edge of G+if and only if G contains a path from v to w of the form (v, x1, x2, …, xk, w) with xi < min(v, w) for each i.
(This includes the possibility k = 0, in which case (v, w) is an edge of G and therefore of G+.)
(i, k) ; (i, p(k)) ; (i, p(p(k))) ; (i, p(p(p(k)))) . . .