Blendstrings: an environment for computing with smooth functions
arXiv:2305.11076
Abstract
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.
16 pages, 3 figures, accepted to Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023