Scientific Computing

This module demonstrates Newton's method for minimizing a nonlinear function in one dimension. Given an appoximate solution value, a new approximate solution value is given by the minimum of a quadratic polynomial interpolating the objective function and its first and second derivatives at the given point. The process is repeated until convergence, which is usually very rapid. The method is equivalent to applying Newton's method to compute a zero of the derivative of the objective function.

The user selects a problem either by choosing a preset example or
typing in a desired objective function *f*(*x*)*x*. The steps of Newton's method are then
carried out sequentially by repeatedly clicking on NEXT or on the
currently highlighted step. The current point *x* and
corresponding function value *f*(*x*)*p*(*x*)

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 6.4.3, especially Algorithm 6.2 and Example 6.10.

**Developers:** Jeffrey Naisbitt and Michael Heath