Homework assigned 11/10, due 11/17
Section 8.3
Problems 5, 6, 10, 16, 17
Section 8.4
Problem 6
Write a program pent_diag.m to solve a pentadiagonal problem. Look here for the desired notation.
Test it on a randomly made n by n matrix for n = 5, 10, 20, 50, and
100. Make sure it gets the right answer by presenting
max(abs(A*x-b)). For each value of n, find the number of flops your
pentadiagonal solver took. Find a polynomial in n that gives the
number of flops it took. Repeat the problem using the gaussian
elimination solver. Find a polynomial in n that gives the number of
flops it took.
Section 8.5
Problems 1c, 2, 3, 7
For #2, if you are having problems proving the inequalities
in general, then start by checking that they hold for the
special cases of:
x = [1;-1], y = [2;-2], z = [-3;3]
A = [1,-2;-4,1], B = [3,-8;1,-1].