This module demonstrates how the same polynomial can be expressed in different ways as a linear combination of various sets of basis functions. It also gives insight into some of the differences among several common polynomial bases
The user first chooses a target polynomial
Certain characteristics of the available polynomial bases are illustrated here. The monomial basis is built as a succession of Taylor polynomial approximations around zero. The Lagrange basis functions have the property of taking either the value 0 or 1 at the interpolation points. The Newton basis functions take the value 0 at all previously interpolated points. The orthogonal Chebyshev basis functions minimize the maximum error over the interval of interpolation, often getting a good approximation to the target polynomial with fewer basis functions than the other bases.
Reference: Michael T. Heath, Scientific Computing, An Introductory Survey, 2nd edition, McGraw-Hill, New York, 2002. See Section 7.3.
Developers: Evan VanderZee and Michael Heath