Polynomial Chaos Confined to the Unit Circle
Abstract
Polynomial chaos expresses a probability density function (pdf) as a linear combination of basis polynomials. If the density and basis polynomials are over the same field, any set of basis polynomials can describe the pdf; however, the most logical choice of polynomials is the family that is orthogonal with respect to the pdf. This problem is well-studied over the field of real numbers, but has yet to be extended to the field of complex numbers. This extension would make polynomial chaos a feasible choice for representing angular random variables, which are confined to the complex unit circle. A method of performing polynomial chaos expansions on angular random variables is developed using the Szegö polynomials as the orthogonal basis. This expansion provides an alternate method for propagating a circular pdf that does not require a distribution assumption. The accuracy of the expansion, and its ability to propagate a pdf, is tested by comparing the first two raw moments estimated using polynomial chaos against the analytic values.
Recommended Citation
C. L. Schmid and K. J. DeMars, "Polynomial Chaos Confined to the Unit Circle," Advances in the Astronautical Sciences, vol. 167, pp. 2239 - 2256, Springer, Jan 2018.
Department(s)
Mechanical and Aerospace Engineering
International Standard Book Number (ISBN)
978-087703657-9
International Standard Serial Number (ISSN)
0065-3438
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Springer, All rights reserved.
Publication Date
01 Jan 2018
