Evaluating Polynomials Over the Unit Disk and the Unit Ball
Abstract
We investigate the use of orthonormal polynomials over the unit disk B2 in R2 and the unit ball B3 in R3. An efficient evaluation of an orthonormal polynomial basis is given, and it is used in evaluating general polynomials over B2 and B3. 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.
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