How to calculate the growth order of an algorithm?

Question

Mathematics

Let's say two algorithms are given: Golden section method and Bisection method , how to find their growth order (by the number of steps)?

Answer 1

Your algorithms are essentially the same thing. Just in the first segment is divided in proportion to the golden section, and in the second case, the segment is divided in half.
Both have O(log n) complexity.

Answer 2

If the question is how exactly the complexity estimate for an arbitrary algorithm is derived, then google about the Computational Complexity of Algorithms, Complexity Theory.
Something like this: www.structur.h1.ru/ocenka.htm