MA/CS/EGR 537 Assignment 5 Answers/Grading

MA/CS/EGR 537: Assignment 5 Answers/Grading

p. 86, 4 (a) x^N - A = 0 implies that x = A^1/N. There is a solution unless N is even and A is less than 0. In fact, there is a solution at both -x or +x when N is even.
(b) This is computed by calculating the derivative of f(x) = x^N - A, which is f'(x) = Nx^N-1, substituting into

g(x) = x - f(x)/f'(x), and simplying.

Point Loss: -5 for not identifying which A's and N's produce a root.

p. 86, 6 This was a simple Matlab script that implemented 2 algorithms.

Point Loss: -10 for a method missing.

p. 89, 29 (a) Note that there exists some integer m such that

2^2(m-1) < A < 2^2m for all real A>0. Since A = (A / 2^2m) · 2^2m, define q = (A / 2^2m). Hence, q in [ 2^2(m-1) · 2^-2m, 2^2m · 2^-2m ) = [ ¼, 1 ).

Point Loss: -10 if there is a rigorous proof of (a) missing or you assume that ¼<q<1 without a proof.

Cheers,
Craig C. Douglas