### Homework due Thursday 2/25

### Please go over the two diaries on gaussian
elimination and LU decompositions!

Make a flop-count table as follows:

Choose a random 10 by 10
matrix. Solve Ax=b for N vectors b. Present the number of flops used
as a function of N. (See the diary for how to do flop counts.) Now
solve A x = b for N vectors b by first doing an LU decomposition and then
using it to solve A x = b. Present the number of flops used as a
function of N when doing it this way.

At what value of N does the
LU decomposition become faster?

For the gaussian elimination,
the number of flops = N * f(n). Find f(n) as a function of n by
varying the size of the problem.

For the LU decomposition,
the number of flops = g(n) + N*h(n). Find g(n) and h(n) by varying
the size of the problem.

Use this information to find
N_crit(n), the value at which it's faster to do the LU decomposition
rather than the Gaussian elimination.