{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

SymmetricOrdering

# SymmetricOrdering - Administrivia Administrivia No class...

This preview shows pages 1–6. Sign up to view the full content.

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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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) [chordal] Symmetric Gaussian elimination: for j = 1 to n add edges between j’s higher-numbered neighbors Fill : new nonzeros in factor

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}