Interactive Educational Modules in
Scientific Computing

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