Create faster Fibonacci function for n > 100 in MATLAB / octave

Question

I have a function that tells me the nth number in a Fibonacci sequence. The problem is it becomes very slow when trying to find larger numbers in the Fibonacci sequence doe

Answer 1

Seems like fibonaacci series follows the golden ratio, as talked about in some detail here.

This was used in this MATLAB File-exchange code and I am writing here, just the esssence of it -

sqrt5 = sqrt(5);
alpha = (1 + sqrt5)/2;   %// alpha = 1.618... is the golden ratio
fibs  = round( alpha.^n ./ sqrt5 )

You can feed an integer into n for the nth number in Fibonacci Series or feed an array 1:n to have the whole series.

Please note that this method holds good till n = 69 only.