MATLAB script to perform functional iteration to estimate the positive root to
within an absolute error τ = 10−10. We use the a posteriori bound to decide
when to stop. We use the following example
Consider the function g (x) ≡ x − 2 tan−1 (x).
This function has three roots: a trivial root at zero, and two others. Because of the odd symmetry of g, the two nonzero roots differ only by a sign;
call them ±x*We will consider functional iteration: x(n+1)= f (xn)
with f (x) ≡ 2 tan−1(x) as a method to solve the equation g (x) = 0.
G M Fahad Bin Mostafa (2021). functional iteration with posteriori bound (https://www.mathworks.com/matlabcentral/fileexchange/74079-functional-iteration-with-posteriori-bound), MATLAB Central File Exchange. Retrieved .
Eugene Isaacson and Herbert Bishop Keller. Analysis of numerical methods. Courier Corporation, 2012
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