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Values from the iteration x = cos(x) are:
x0 = 0.8, x1 = 0.696707, x2 = 0.766959, x3 = 0.720024, x4 = 0.751790, x5 = 0.730468.
a) Calculate the sequence {yn} from Aitken's ?2 method. Given that the solution of x = cos x is 0.739085133 . . . , ?nd the rations between consecutive errors in {xn} (which approach a constant A) and also in {yn} (which approach another constant, say B). Con?rm that {yn} is converging twice as fast as {xn} (i.e. that B = A2).
b) Use Steffensen's method: from x0, x1, x2 calculate y0. Then start the iteration again from x3 = y0, and from x3, x4, x5 calculate y1.
From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r
I have some work in Mupad i need doing. Its on Diff equations. Canb you guys help?
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