Problem A1 for homework due Monday 31 January 2005

This is just a little experiment for you to do in
Matlab.  Turn in the diary from your session and
the answers to the questions.

Load the file "temperature.mat", which is linked
from the course web page, into Matlab.  It contains
the matrix A100 that we used in class on Jan 24.

Create a right-hand side vector b with 10000 entries,
of which the first 100 are equal to 100 and the rest
are zero.

You can measure the time a Matlab command takes 
with "tic" and "toc".  

(A1.1) Say to Matlab, all on one line:

>> tic; t = A100 \ b; toc;

Repeat this a couple of times.  How long does Matlab
take to solve the linear system?

(A1.2) Now say

>> tic; R = chol(A100); toc;

a few times.  How long does Matlab take to compute 
this Cholesky factor?  If this is significantly 
different from the previous test, can you guess why?

(A1.3) Now say

>> tic; p = symamd(A100); R = chol(A100(p,p)); toc;

Can you explain the results?

(A1.4) How many nonzeros do chol(A100) 
and chol(A100(p,p)) have?