(1a, September 5. Will be collected with 1b at the end of the month)
Code the Jacobi method to solve the linear system Au=b, where
A is a matrix with -2 down the diagonal, 1 on the sub- and super-diagonals, and
b=0. Fix the conditions 
(start with 0 and 1 resp). You can
solve the equation exactly, to test your code. The question to address is When to
stop iterating? For purposes here, compute the residual 
, and iterate
until 
is small. We'll be more precise as the semester proceeds.
(1b, September 12. To be collected with 1a on Sept. 26) Given an invertible matrix A, the matrix iteration
will converge to A^-1. One effective choice of X^0 is a scaled transpose of A, namely
and s is a scale factor greater than 1, and 
.
Using the same A as in part 1a, solve Au=b by (approximately) inverting A according to this iteration.
Compare the number of operations each method involves. Use the time command to get an idea of how each method scales as you increase from say O(10^2) to O(10^4) components.
See COR502 notes and references therein.
November 14-16 Dr. Jeff Tilson of CCR will present 2 lectures, discussing the IBM SP and parallel debugging.
Nov 30. Professor Ken Hoffmann of the School of Medicine will be speaking at the coloquium. abstract
PROJECT Foxes, rabbits and grass. DUE December 11,4:30 p.m. turn work
into my mailbox in the math department.