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In Inverse Problem for Trigonometric Polynomials: Does the Distribution of a Homogeneous Polynomial in a Gaussian Random Point Define the Polynomial?

โœ Scribed by Y.M. Baryshnikov; W. Stadje

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
882 KB
Volume
15
Category
Article
ISSN
0196-8858

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โœฆ Synopsis

It is shown that the probability distribution of the value of a homogeneous polynomial in two Gaussian variables determines the polynomial up to some explicitly described ambiguity, if the degree of the polynomial is five or less, or for generic polynomials of arbitrary degree. 1994 Academic Press, Inc.

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## Abstract A new procedure for characterizing the solution of the eigenvalue problem in the presence of uncertainty is presented. The eigenvalues and eigenvectors are described through their projections on the polynomial chaos basis. An efficient method for estimating the coefficients with respect