SymmetricOrdering

SymmetricOrdering - Administrivia: October 12, 2009...

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Administrivia: October 12, 2009 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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Administrivia: October 19, 2009 Administrivia: October 19, 2009 Homework 3 on web site today, due Wed Oct 28 Reading in Davis: Chapter 8: putting it all together to solve Ax = b
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Graphs and Sparse Matrices Graphs and Sparse Matrices : Cholesky factorization : Cholesky factorization 10 1 3 2 4 5 6 7 8 9 10 1 3 2 4 5 6 7 8 9 G(A) G + (A) Symmetric Gaussian elimination: for j = 1 to n add edges between j’s higher-numbered neighbors Fill : new nonzeros in factor
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Heuristic fill-reducing matrix permutations Heuristic fill-reducing matrix permutations Nested dissection: Find a separator, number it last , proceed recursively Theory: approx optimal separators => approx optimal fill and flop count Practice: often wins for very large problems Minimum degree: Eliminate row/col with fewest nzs, add fill, repeat Hard to implement efficiently – current champion is “Approximate Minimum Degree” [Amestoy, Davis, Duff] Theory: can be suboptimal even on 2D model problem Practice: often wins for medium-sized problems Banded orderings (Reverse Cuthill-McKee, Sloan, . . .): Try to keep all nonzeros close to the diagonal Theory, practice: often wins for “long, thin” problems The best modern general-purpose orderings are ND/MD hybrids.
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Fill-reducing permutations in Matlab Fill-reducing permutations in Matlab Symmetric approximate minimum degree: p = amd(A); symmetric permutation: chol(A(p,p)) often sparser than chol(A) Symmetric nested dissection: not built into Matlab
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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.

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SymmetricOrdering - Administrivia: October 12, 2009...

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