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
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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. |
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a is the left point of the bracketing interval. The default is 0.0. |
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b is the middle point of the bracketing interval. The default is 0.0. |
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c is the right point of the bracketing interval. The default is 0.0. |
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formula is a string describing the function under investigation. The Formula VIs check the syntax of this string. |
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minimum is the determined local minimum of formula. |
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f(minimum) is the function value at the determined local minimum. |
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ticks is the time in milliseconds for the whole calculation. |
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error returns any error or warning condition from the VI. |
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).