Scientific Computing

This module demonstrates the convergence (or nonconvergence) of the polynomial interpolants to a given continuous function as the number of interpolation points, and hence the degree of the interpolating polynomial, grows.

The user chooses the function to be interpolated, the number of
interpolation points, and whether the locations of the points are to be
either equally spaced or at the Chebyshev points. The chosen function
and polynomial interpolant are plotted along with two error bounds.
The polynomial interpolant must always lie within the shaded area
defined by either error bound. For a description of the error bounds,
see the error bound module. For the first
example, Runge's function *f*(*x*) = 1 ⁄
(1+25*x*^{2}),*f*(*x*) = 1
− | *x* |,

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 7.3.5, especially Figures 7.7 and 7.8.

**Developers:** Evan VanderZee and Michael Heath