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Polynomial chaos for the approximation of uncertainties: Chances and limits

Published online by Cambridge University Press:  01 April 2008

Technical University of Munich, Department of Mathematics, 85748 Garching, Germany email:;
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81730 Munich, Germany email:;;
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81730 Munich, Germany email:;;
Technical University of Munich, Department of Mathematics, 85748 Garching, Germany email:;
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81730 Munich, Germany email:;;


In technical applications, uncertainties are a topic of increasing interest. During the last years the Polynomial Chaos of Wiener (Amer. J. Math. 60(4), 897–936, 1938) was revealed to be a cheap alternative to Monte Carlo simulations. In this paper we apply Polynomial Chaos to stationary and transient problems, both from academics and from industry. For each of the applications, chances and limits of Polynomial Chaos are discussed. The presented problems show the need for new theoretical results.

A Survey in Mathematics for Industry
Copyright © Cambridge University Press 2008

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