Lowering the Golden Ratio: The Impact on Golden Section Search Efficiency

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The discussion centers on comparing the efficiency of the golden section search and interval bisection search methods for optimizing the function y = x^2. It was observed that the golden section search required approximately twice as many iterations as the interval bisection search. However, adjusting the golden ratio from 0.618 to 0.5562 resulted in a reduction of iterations from 40 to 32, suggesting that a lower ratio can enhance the efficiency of the golden section search. The conversation raises questions about the reasons behind this improved performance and seeks to clarify the advantages of the golden section search over the interval bisection method, particularly in terms of its application for finding maxima or minima within a specified range. Additionally, inquiries are made regarding the specific range of x being analyzed and the extremes that need to be identified within that range.
Prinzmio
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Currently my task is to count number of iterations of golden section search verus interval bisection search of a function y = x^2. Golden section search took about twice the number of iterations than interval bisection search.

If I lowered the golden ratio from 0.618 to 0.5562 , the number of iterations get improved, from 40 iterations to 32.

Could you please advise, why lowering golden ratio improves efficiency of golden section search? If lowering ratio means better performance, what is the advantage of Golden section search verus interval bisection search?
 
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A golden-section search is used to find a maximum or a minimum over a specified range.
Over what range of x are you searching?
What extreme is there to find in the range?
 

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