CS 340 -- Section 01, Fall 2001, Ridgway Scott

Parallel Scientific Computing Assignment due 27 Nov 01

Read Chapter 11 of the notes and work the following problems

• Re-do the program in Ex. 13.5 for doing Gaussian elimination with the following test matrix:
  1 1 1 1 1 1 1 1 1 . . .
  1 2 2 2 2 2 2 2 2 . . .
  1 2 3 3 3 3 3 3 3 . . .
  1 2 3 4 4 4 4 4 4 . . .
  1 2 3 4 5 5 5 5 5 . . .
  1 2 3 4 5 6 6 6 6 . . .
  1 2 3 4 5 6 7 7 7 . . .
  1 2 3 4 5 6 7 8 8 . . .
  1 2 3 4 5 6 7 8 9 . . .
  . . . . . . . . . . . . . . . . .
  Run this with n=1024 on 1, 2, 4, 8 and 16 processors and make a logarithmic performance prediction plot of the timing results.

  (Don't forget How to do parallel performance analysis.)

  Test your code by checking to see if the resulting matrix U is all ones on and above the diagonal (compute and print the sum of squares of differences between U_{ij} and 1 for the appropriate i and j. If you compute L, do the same for L (but the lower triangle are all ones: L=U' .)
  For extra credit, run this with n=2048 on 2, 4, and 8.

• Ex. 13.33
• Program the parallel prefix algorithm for solving (13.35) in Chapter 13.