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

Click For Summary
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
Messages
1
Reaction score
0
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?
 
Technology news on Phys.org
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?
 

Thread 'For those who ask: "What programming language should I learn?"'

Learn If you want to write code for Python Machine learning, AI Statistics/data analysis Scientific research Web application servers Some microcontrollers JavaScript/Node JS/TypeScript Web sites Web application servers C# Games (Unity) Consumer applications (Windows) Business applications C++ Games (Unreal Engine) Operating systems, device drivers Microcontrollers/embedded systems Consumer applications (Linux) Some more tips: Do not learn C++ (or any other dialect of C) as a...
View full post »

Similar threads

Gradient descent, anything better than golden section line search
  • · Replies 1 ·
Replies
1
Views
4K
Is LCEVC the Solution for Efficient 8K Television Compression?
  • · Replies 4 ·
Replies
4
Views
2K
I Updates on the experiments X17
  • · Replies 50 ·
2
Replies
50
Views
10K
AlphaEvolve - The Future of Math?
  • · Replies 4 ·
Replies
4
Views
535
Writing: Input Wanted Generation Ship SFV Exodus: Revised Designs
  • · Replies 52 ·
2
Replies
52
Views
7K
New CRISPR-based tool for find-and-replace editing of DNA
  • · Replies 2 ·
Replies
2
Views
4K
Requesting suggestions for languages, libraries, and architectures for parallel (and sometimes non parallel) numerical and scientific computations
  • · Replies 8 ·
Replies
8
Views
4K
Blueshift + Classical Physics = Golden Ratio
  • · Replies 3 ·
Replies
3
Views
3K
Programs How good is this applied math program?
  • · Replies 13 ·
Replies
13
Views
3K
I Progress In Calculating The HLbL Contribution To Muon g-2
  • · Replies 0 ·
Replies
0
Views
2K