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

In summary, the conversation discusses the comparison between golden section search and interval bisection search in terms of number of iterations. It is mentioned that lowering the golden ratio can improve the efficiency of golden section search, leading to fewer iterations. This raises the question of why this is the case and what advantage golden section search has over interval bisection search. Additionally, the conversation mentions that a golden-section search is used to find a maximum or minimum over a specified range and asks about the specific range and extreme being searched for.
  • #1
Prinzmio
1
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?
 
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  • #2
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?
 

1. What is the golden ratio and how is it related to search efficiency?

The golden ratio is a mathematical constant, approximately equal to 1.618, that has been found to have aesthetic and mathematical significance. In terms of search efficiency, it is used in the golden section search algorithm to find the optimal value of a function within a specified range.

2. How does lowering the golden ratio impact search efficiency?

Lowering the golden ratio in the golden section search algorithm can improve search efficiency by reducing the number of function evaluations needed to find the optimal value. This is because a smaller golden ratio means that the search interval is divided into smaller segments, leading to a more precise and efficient search.

3. Are there any potential drawbacks to lowering the golden ratio?

While lowering the golden ratio can improve search efficiency, it may also lead to a slower convergence rate. This means that the algorithm may take longer to find the optimal value compared to using a higher golden ratio. Additionally, using a very small golden ratio may result in a more complex and computationally intensive algorithm.

4. What factors should be considered when determining the optimal value for the golden ratio?

The optimal value for the golden ratio in the golden section search algorithm depends on various factors, such as the complexity of the function being evaluated, the desired level of precision, and the available computational resources. It is important to strike a balance between search efficiency and convergence rate when choosing the golden ratio.

5. Are there any other search algorithms that can be used to improve efficiency?

Yes, there are various other search algorithms that can be used to improve efficiency, such as the gradient descent method, the Newton-Raphson method, and the simulated annealing algorithm. The choice of algorithm depends on the specific problem and the desired level of efficiency and accuracy.

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