Blendstrings: an environment for computing with smooth functions
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.
Cite
@article{arxiv.2305.11076,
title = {Blendstrings: an environment for computing with smooth functions},
author = {Robert M. Corless},
journal= {arXiv preprint arXiv:2305.11076},
year = {2023}
}
Comments
16 pages, 3 figures, accepted to Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023