How to use Matrix Market matrices in Matlab

1. How to use Matrix Market matrices in Matlab The Matrix Market is an interesting collection of matrices from a variety of applications

2. 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

3. 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)

5. 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)

6. The structure of sparse matrices

7. Time and accuracy of solving a system of equations

8. Non-zero structure of A

9. Fill-in

10. Fill-in

11. Column reordering

13. The value of sparsity

14. 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