Scientific Computing

This module demonstrates the linear fractional interpolation method for
solving a nonlinear equation *f*(*x*) = 0

The user selects a problem either by choosing a preset example or
typing in a desired function *f*(*x*). The user can also
select starting points *x* or accept default values. The
successive steps of the linear fractional interpolation method are then
carried out sequentially by repeatedly clicking on NEXT or on the
currently highlighted step. The current values of *x* and
*f*(*x*) are indicated by bullets on the plot and are also
shown numerically in the table below. At each iteration of the linear
fractional interpolation method, a rational function is fit to the
three current values of *f*(*x*), the next approximate
solution is taken to be the zero of the rational function, and the
process is then repeated. If the starting guesses are close enough to
the true solution, then the linear fractional interpolation method
converges to it, typically with a superlinear convergence rate.

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 5.5.6, especially Example 5.14.

**Developers:** Jeffrey Naisbitt and Michael Heath