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

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SUMMARY

The discussion focuses on the efficiency of the Golden Section Search algorithm compared to the Interval Bisection Search when applied to the function y = x^2. Lowering the golden ratio from 0.618 to 0.5562 resulted in a reduction of iterations from 40 to 32, demonstrating improved efficiency. The Golden Section Search is specifically designed to find extrema within a specified range, making it advantageous for optimization tasks. The discussion highlights the importance of the golden ratio in determining the efficiency of the search process.

PREREQUISITES
  • Understanding of optimization algorithms, specifically Golden Section Search and Interval Bisection Search.
  • Familiarity with the mathematical function y = x^2.
  • Knowledge of the concept of the golden ratio in search algorithms.
  • Basic principles of iterative methods in numerical analysis.
NEXT STEPS
  • Research the mathematical foundations of the Golden Section Search algorithm.
  • Explore the differences in convergence rates between Golden Section Search and Interval Bisection Search.
  • Learn about the implications of varying the golden ratio in optimization problems.
  • Investigate other optimization techniques and their performance metrics.
USEFUL FOR

Mathematicians, algorithm developers, and optimization specialists interested in enhancing search efficiency in numerical methods.

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?
 
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?
 

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