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

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