Analysis of Discrete $$L^2$$ L 2 Projection on Polynomial Spaces with Random Evaluations
نویسندگان
چکیده
منابع مشابه
Analysis of the discrete L2 projection on polynomial spaces with random evaluations
We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the monovariate case, when the observation ...
متن کاملAnalysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations
We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points...
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In this work we consider the random discrete L 2 projection on polynomial spaces (hereafter RDP) for the approximation of scalar Quantities of Interest (QOIs) related to the solution of a Partial Differential Equation model with random input parameters. The RDP technique consists of randomly sampling the input parameters and computing the corresponding values of the QOI, as in a standard Monte ...
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∗ Corresponding author. E-mail addresses: [email protected] (G. Migliorati), [email protected] (F. Nobile). http://dx.doi.org/10.1016/j.jco.2015.02.001 0885-064X/© 2015 Published by Elsevier Inc. 518 G. Migliorati, F. Nobile / Journal of Complexity 31 (2015) 517–542
متن کاملDiscrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [8] and in probability in [20], under suitable condition...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2014
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-013-9186-4