ECOR 2606 Lecture Notes - Iter, Bisection Method, Golden Ratio
28 Sep 2014
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Document Summary
Very similar in concept to a bisection search. To get started we need a pair of x values that bracket the solution. At each iteration the interval containing the solution gets smaller and smaller. By continuing until the interval becomes appropriately small any desired degree of accuracy can be achieved. As f(xa) f(xb) , the low wall is moved up (xlow = xa) The process continues until the walls are sufficiently close that the midpoint is guaranteed to be within the desired tolerance of the minimum. At this point we take the midpoint as our final estimate and call it quits. On each iteration the interval is reduced by a factor of 0. 51 (nearly as good as bisection). Assuming that the interval midpoint is taken as the final answer, the maximum possible error after n wall movements is.
