Evaluating Polynomials Over the Unit Disk and the Unit Ball
Numerical Analysis
2013-08-09 v2
Abstract
We investigate the use of orthonormal polynomials over the unit disk B_2 in R^2 and the unit ball B_3 in R^3. An efficient evaluation of an orthonormal polynomial basis is given, and it is used in evaluating general polynomials over B_2 and B_3. The least squares approximation of a function f on the unit disk by polynomials of a given degree is investigated, including how to write a polynomial using the orthonormal basis. Matlab codes are given.
Cite
@article{arxiv.1307.5923,
title = {Evaluating Polynomials Over the Unit Disk and the Unit Ball},
author = {Kendall Atkinson and Olaf Hansen and David Chien},
journal= {arXiv preprint arXiv:1307.5923},
year = {2013}
}
Comments
19 pages, 3 figures