Basic Idea
The diagram above illustrates a single step in the technique for finding a minimum. The functional values of are on the vertical axis, and the horizontal axis is the x parameter. The value of has already been evaluated at the three points:, and . Since is smaller than either or, it is clear that a minimum lies inside the interval from to (since f is unimodal).
The next step in the minimization process is to "probe" the function by evaluating it at a new value of x, namely . It is most efficient to choose somewhere inside the largest interval, i.e. between and . From the diagram, it is clear that if the function yields then a minimum lies between and and the new triplet of points will be, and . However if the function yields the value then a minimum lies between and, and the new triplet of points will be, and . Thus, in either case, we can construct a new narrower search interval that is guaranteed to contain the function's minimum.
Read more about this topic: Golden Section Search
Famous quotes related to basic idea:
“The basic idea which runs right through modern history and modern liberalism is that the public has got to be marginalized. The general public are viewed as no more than ignorant and meddlesome outsiders, a bewildered herd.”
—Noam Chomsky (b. 1928)