Nonlinear Opt.: Gold section search 2: Unterschied zwischen den Versionen
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Let a and b be the end points of the initial interval. Compute the intermediate points: | Let a and b be the end points of the initial interval. Compute the intermediate points: | ||
| − | <math>x_{1 | + | <math>x_{1}=a+\frac{b-a}{(1,618)^{2}}</math> |
Version vom 20. Juni 2013, 16:24 Uhr
The Golden Section Search is an Algorithm/ technique for finding the extremum of an unimodal function over an interval without using derivatives. It is very clever. The advantage towards other section search methods is the need of only one new evaluation instead of two, because one intermediate points is the same as in the previous iteration. Fetter TextThe name of the search methods is based on the calculation of the two intermediate points by using the golden ratio.
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): Golden Ratio: \phi=\frac{a}{b}=\frac{1+\sqrt{5}}{2}= 1,618
Golden section algorithm
Step one: Let a and b be the end points of the initial interval. Compute the intermediate points:
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): x_{1}=a+\frac{b-a}{(1,618)^{2}}
