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,. ..,N1] with n not equal to m, then the sum from k=0 to k=N1 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,. ..,N1, we have that the sum from k=0 to k=N1 of f(k)*cas(n*k/N) equals the sum from k=0 to k=M1 of f(2*k)*cas(n*k/M) plus the sum from k=0 to k=M1 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.
 Fall '09
 Wickerhauser
 Math, Applied Mathematics, Addition

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