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Generalized polynomial chaos expansions with weights.

J. Comput. Anal. Appl. 18, 30-45 (2015)
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Polynomial chaos is used as an alternative to Monte Carlo methods for the propagation of uncertainty through dynamical systems. By truncating the infinite series of the polynomial chaos expansion to a finite order, the positivity of the approximate solution may be lost. We show in general how the positivity can be preserved by introducing weights into the finite polynomial approximation, where the polynomial systems are assumed to have compact support. In the case of Legendre polynomials examples of such weights are given explicitly.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Polynomial Chaos ; Orthogonal Polynomials ; Legendre Polynomials ; Positive Operators ; Dynamical Systems; Approximation
ISSN (print) / ISBN 1521-1398
e-ISSN 1572-9206
Quellenangaben Volume: 18, Issue: 1, Pages: 30-45 Article Number: , Supplement: ,
Publisher Eudoxus Press
Reviewing status Peer reviewed