Ma 449: Numerical Applied Mathematics
		      Reading and Homework Assignment 6
		      Due: Monday, October 17th, 2011
			     Prof. Wickerhauser

You are encouraged to collaborate on homework, and to work additional
exercises from the indicated problem sections, although the homework grade
will be based only on the exercises listed below.  Please return your
solutions to me by the end of class.  LATE HOMEWORK WILL NOT BE ACCEPTED.

Check your solutions to problems marked with an asterisk(*) against the
values in the textbook's Answers section, pp.646--672.

Read Chapter 5, Sections 5.1 to 5.5, of the text.

Do Exercise 2(b) of Section 5.1, p.259.
Do Exercise 5 of Section 5.1, p.260.
Do Exercise 6 of Section 5.1, p.260.
Do Algorithm 4(a,b,c) of Section 5.1, p.262.

Do Exercise 2(c) of Section 5.2, p.275.
Do Exercise 12 of Section 5.2, p.277.

Do Exercise 2(a,b) of Section 5.3, p.294.
Do Algorithm 5 of Section 5.3, p.297.

Do Exercise 2 of Section 5.4, p.307.
Do Exercise 7 of Section 5.4, p.307.

Do Algorithm 1 of Section 5.5, p.319.
Do Algorithm 2 of Section 5.5, p.319.


For the next two problems, set cas(x)= cos(2*PI*x)+sin(2*PI*x).

Problem H06.1. Fix N and show that, if n and m are in the range [0,1,...,N-1]
with n not equal to m, then the sum from k=0 to k=N-1 of
cas(n*k/N)*cas(m*k/N) equals 0.  What is the value when n=m?

Problem H06.2. Show that, for N=2M and any function f=f(k) defined on
0,1,...,N-1, we have that the sum from k=0 to k=N-1 of f(k)*cas(n*k/N) equals
the sum from k=0 to k=M-1 of f(2*k)*cas(n*k/M) plus the sum from k=0 to k=M-1
of f(2*k+1)*cas(n*k/M + n/2M).