Golden Section 1D (Not in Base Package)

Determines a local minimum of a given 1D function with the help of a bracketing of the minimum. The Golden Section Search method is used. Details

accuracy controls the accuracy of the determined minimum of formula. The method stops if two consecutive approximations differ not more than the value of accuracy.
a is the left point of the bracketing interval. The default is 0.0.
b is the middle point of the bracketing interval. The default is 0.0.
c is the right point of the bracketing interval. The default is 0.0.
formula is a string describing the function under investigation. The Formula VIs check the syntax of this string.
minimum is the determined local minimum of formula.
f(minimum) is the function value at the determined local minimum.
ticks is the time in milliseconds for the whole calculation.
error returns any error or warning condition from the VI.

Golden Section 1D Details

A bracketing triplet (a, b, c) of a 1D continuous function f is a combination of three points with f(a) > f(b) and f(c) > f(b). This guarantees the existence of a local minimum of f in the interval (a, c).

The Golden Section Search method determines beginning with a bracketing triplet (a ,b, c) a new one with a considerably smaller expansion. Repeating this scheme often yields a good approximation of the local minimum. The new bracketing point is essentially calculated by the following equation.

(Golden Section Search Method)

The following diagram shows the relationship between a, b, c and f(a), f(b), f(c).