MA/CS/EGR 537: Assignment 4

This is due Tuesday, October 21 in class. Please e-mail your Matlab script(s) to

douglas@ccs.uky.edu

Part I: Sparse Matrices

Write a Matlab script to compute Ax for a matrix A stored in the IJA/AM very modified column sparse matrix format (R. E. Bank and R. K. Smith, General sparse elimination requires no permanent integer storage, SIAM J. Sci. Stat. Comp., 8 (1987), pp. 574-584). Use your conjugate gradient code from Assignment 3 to compute the solution using the sparse matrix IJA/AM. (Make a copy of your code from Assignment 3 before you begin.)

• Be efficient and compute Ax once per iteration.
• Use the forms of alpha and beta which use the least amount of computing.
• Minimize the number of flops.
• Be efficient when setting up the IJA and AM vectors.
• Do not have a dense matrix A left in your new code.

• How many iterations did you use? Was it the same as in assignment 3? (If not, why not?)
• How many flops did you use per iteration? (You can print the variable flops each iteration and before the iterations start to determine this information.)

Instead of using n=4, as in Assignment 3, now use n=50. You will have a matrix of order 2500 instead of 16. (Do not print anything other than the residual norm per iteration.) How many iterations does it take to reduce the residual norm by 10^-6?

I have placed a sample matrix A, AM, and IJA in a hints file.

Part II: Roots of Equations

From the text, do the following:

Page	Problem
64	11
64	16
64	19

Cheers,
Craig C. Douglas