Tuning orthogonal polynomial degree and segment interval length to achieve prescribed precision approximation of irregular functions

Ahmed M. Atallah, Robyn M. Woollands, Ahmad Bani Younes, John L. Junkins

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The orthogonal Chebyshev polynomials are commonly used to approximate functions. The approximation accuracy is dependent on the nature of the approximated function, its domain, the Chebyshev series degree, and the number sampling nodes. In this paper, we show how to optimally choose the degree of Chebyshev expansion to achieve a prescribed accuracy. The error is estimated by comparing the value of the function and its Chebyshev-based approximation at equidistant nodes. For regular functions, a quasi-linear relation could be constructed between the number of accurate significant figures of the interpolated values at uniform nodes and the degree of the Chebyshev series. Moreover, the paper studies the generalization of this quasi-linear relation for irregular functions.

Original languageEnglish (US)
Title of host publicationSpace Flight Mechanics Meeting
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
Edition210009
ISBN (Print)9781624105333
DOIs
StatePublished - 2018
Externally publishedYes
EventSpace Flight Mechanics Meeting, 2018 - Kissimmee, United States
Duration: Jan 8 2018Jan 12 2018

Publication series

NameSpace Flight Mechanics Meeting, 2018
Number210009

Other

OtherSpace Flight Mechanics Meeting, 2018
CountryUnited States
CityKissimmee
Period1/8/181/12/18

ASJC Scopus subject areas

  • Aerospace Engineering

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