Scientific Computing

This module demonstrates successive parabolic interpolation for minimizing a nonlinear function in one dimension. Given three approximate solution values, a new approximate solution value is given by the minimum of a quadratic polynomial interpolating the three given approximate solution values. The new approximate solution value replaces one of the old ones, and the process is repeated until convergence, which is usually quite rapid.

The user selects a problem either by choosing a preset example or
typing in a desired objective function *f*(*x*)*x*_{0}, *x*_{1},
*x*_{2}. The steps of successive parabolic interpolation
are then carried out sequentially by repeatedly clicking on NEXT or on
the currently highlighted step. The current points *x* and
corresponding function values *f*(*x*)*p*(*x*)

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 6.4.2, especially Example 6.9.

**Developers:** Jeffrey Naisbitt and Michael Heath