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How to use Matrix Market matrices in Matlab The Matrix Market is an interesting collection of...
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Transcript of How to use Matrix Market matrices in Matlab The Matrix Market is an interesting collection of...
How to use Matrix Market matrices in Matlab
The Matrix Market is an interesting collection of matrices from a variety of applications
Purpose
• To illustrate the use of Matrix Market matrices in Matlab
• To learn a bit about sparse matrices
• To use some of the tools available in Matlab for working with sparse matrices
Preliminary Steps• Locate a matrix at the Matrix Market web site
math.nist.gov/MatrixMarket (see the “Introduction to the Matrix Market” tutorial)
• Download and uncompress a file describing the matrix (see the “Downloading matrices from the Matrix Market” tutorial)
• Load the matrix into Matlab (see “Converting Matrix Market matrices to Matlab” tutorial and this tutorial)
In Matlab we will illustrate
• The structure of sparse matrices (using spy)• Solving large linear systems (using \)• The time required (using tic and toc)• The accuracy of the calculated solution (using
norm and condest)• Fill-in in the factorization (using lu, nnz and spy)• The effect of column reordering on fill-in (using
colmmd, lu, nnz and spy)• The time required for the solution when sparsity is
not used (using full)
The structure of sparse matrices
Time and accuracy of solving a system of equations
Non-zero structure of A
Fill-in
Fill-in
Column reordering
The value of sparsity
Other tutorials available at www.math.sjsu.edu/~foster
• Introduction to the Matrix Market
• Downloading matrices from the Matrix Market
• Converting Matrix Market matrices to Matlab format
• Iterative methods in Matlab with Matrix Market matrices