Talk:Golden section search

From Wikipedia, the free encyclopedia

	This article is related to WikiProject Golden ratio, an attempt to write quality articles about the golden ratio in all of its many forms. If you would like to participate, you can edit the article attached to this page, or visit the project page, where you can join the project and contribute to the discussion.
Start	This article has been rated as Start-Class on the assessment scale.
Mid	This article has been rated as Mid-Importance within Schools.
Assessment: Hello all, and thank you for contributing to this article. I'm part of the Wikipedia:WikiProject Golden ratio team, and I'm reviewing this page. I'm currently giving it a grade of Start on the Wikipedia 1.0 Assessment Scale and an importance of Mid on this importance scale. For information on improving this article, please visit the WikiProject Golden ratio Project Page. My reasoning is as follows: Needs expansion and inline references. Adam McCormick (talk) 00:53, 21 March 2008 (UTC)

[edit] Motivation, etc

I have changed a few things on the recent addition.

The motivation previously provided might not be as clear as it could be. I have added a sentence in the beginning. The new motivation was first of all wrong, and secondly, it removed the explanation of the intervals a,b,c in the diagram.

The selection of the "probe" point in the golden ratio does not guarantee the fastest possible convergence. The fastest possible convergence ratio is not known a priori. The selection of the probe point yields a constant narrowing ratio and search interval, so that at each point, no one interval is favored over another in the search.

I think the other additions are excellent. PAR 21:38, 13 February 2007 (UTC)

Hi David - on the recent additions - yes, thats the part that was missing. It looks a lot better. PAR 22:04, 13 February 2007 (UTC)

Thanks — I'm glad we seem to have converged to something we both agree is an improvement. —David Eppstein 22:08, 13 February 2007 (UTC)

[edit] Problem with the Termination Condition section?

I hesitate to make the change myself, but there is clearly at least a notation issue in that section. It starts out by listing x₀, x₁, x₂ and x₃ as the relevant variables, but in the equation we find x₄ and no x₀. In the original text (Numerical Recipes in C, page 402), there is no x₄ and the equation is written as:

as opposed to

in this article. The fact that x₃ didn't change tells me that this is not just an off-by-1 problem. I think the issue arises from the fact that earlier in the article the notation is 1-based, not 0-based. My proposed change would be to list the formula as:

The biggest reason I didn't change it though is the following line that refers to the precision of x₂ and x₃, and I don't know which notation scheme this is referring to (I imagine it's the 1-based one).

(sorry for the deletion in the history - realized I wasn't logged in when I wrote it, wanted to get it put back in my name so I can address comments/questions)