next up previous

Exercise 1: The determination of a minimum of a function.

Consider finding the minimum of the function by the structure described in algorithm 2.1. This nonlinear function is essentially a quadratic function perturbed by small sinusoidal fluctuations. One can use several simple techniques as a first approach to solving this problem. These include graphics, tabulation of function values, and bisection to bracket the interval where a minimum lies.

a) Plot this function.

b) Plot its derivative ; solving for the roots of is a closely related problem to minimizing .

c) Choose various initial points devise descent paths toward the minimum of .

d) Plot your paths toward the minimum and analyze the results.