Algorithms in a General Program

As underscored in the companion Vol. 1 by Buzzi-Ferraris and Manenti (2010a), it is opportune to combine robust and efficient methods in developing a program to solve any problem that requires iterative algorithms. 

In root-finding, Bolzano s method is combined with other efficient methods because of its robustness. Unfortunately, in the case of one-dimensional optimization, neither the robust methods, golden search nor Fibonacci, can be satisfactorily combined with efficient methods. 

The golden section can be seen as a criterion to check the efficiency of an efficient method if the efficient method does not reduce the interval of uncertainty any better than the golden search, the new point is inserted using a different method. 

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