h06 - Do Exercise 2(a,b of Section 5.3 p.294 Do Algorithm 5...

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Ma 449: Numerical Applied Mathematics Reading and Homework Assignment 6 Due: Friday, October 9th, 2009 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.
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Unformatted text preview: 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)....
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This note was uploaded on 05/16/2010 for the course MATH 449 taught by Professor Wickerhauser during the Fall '09 term at Washington University in St. Louis.

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