Evaluating polynomials over the unit disk and the unit ball |
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| Authors: | Kendall Atkinson David Chien Olaf Hansen |
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| Institution: | 1. The University of Iowa, Iowa City, IA, USA
2. California State University, San Marcos, CA, USA
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| Abstract: | We investigate the use of orthonormal polynomials over the unit disk ??2 in ?2 and the unit ball ??3 in ?3. An efficient evaluation of an orthonormal polynomial basis is given, and it is used in evaluating general polynomials over ??2 and ??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. |
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