Chebyshev Polynomials
This module illustrates Chebyshev polynomials, their zeros, and
their extrema.
The Chebyshev polynomials of the selected degree are plotted on the
interval [−1, 1]. By default, all of the Chebyshev
polynomials up to the given degree are plotted, but the user can choose
to plot only the Chebyshev polynomial of highest degree. The
equi-oscillation property of the Chebyshev polynomials is evident: the
extreme function values are all equidistant from the horizontal axis
and alternate in sign. Optionally, the zeros or extrema of the
highest-degree polynomial, called Chebyshev points, can be
displayed. The Chebyshev points correspond to equally-spaced points on
a circle, but their values on the horizontal axis are not equally
spaced. The Chebyshev points have superior properties for polynomial
interpolation.
Reference: Michael T. Heath, Scientific Computing,
An Introductory Survey, 2nd edition, McGraw-Hill, New York,
2002. See Section 7.3.4, especially Figures 7.5 and 7.6.
Developers: Evan VanderZee and Michael Heath
Department of Computer Science