Blendstrings: an environment for computing with smooth functions

05/18/2023
by   Robert M. Corless, et al.
0

A "blendstring" is a piecewise polynomial interpolant with high-degree two-point Hermite interpolational polynomials on each piece, analogous to a cubic spline. Blendstrings are smoother and can be more accurate than cubic splines, and can be used to represent smooth functions on a line segment or polygonal path in the complex plane. I sketch some properties of blendstrings, including efficient methods for evaluation, differentiation, and integration, as well as a prototype Maple implementation. Blendstrings can be differentiated and integrated exactly and can be combined algebraically. I also show applications of blendstrings to solving differential equations and computing Mathieu functions and generalized Mathieu eigenfunctions.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset