Výsledky vyhledávání - "Multivariate Polynomial Approximation"

A SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA Autor NOBILE, F., TEMPONE, R., WEBSTER, C. G.

“…This work proposes and analyzes a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the…”
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A new multivariate quadrature rule for calculating statistical moments of stochastic response Autor Xiao, Qing

“…As a derivative-free algorithm, the multivariate quadrature rule has been widely used to calculate statistical moments of the output of a system with uncertain…”
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AN ANISOTROPIC SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA Autor NOBILE, F., TEMPONE, R., WEBSTER, C. G.

“…This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial differential equations with random coefficients…”
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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data Autor Babuška, Ivo, Nobile, Fabio, Tempone, Raúl

“…This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms…”
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Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients Autor Beck, Joakim, Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raúl

“…In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular,…”
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Optimal polynomial admissible meshes on some classes of compact subsets of Rd Autor Piazzon, Federico

“…We show that any compact subset of Rd which is the closure of a bounded star-shaped Lipschitz domain Ω, such that ∁Ω has positive reach in the sense of…”
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Uniqueness of solutions in multivariate Chebyshev approximation problems Autor Roshchina, Vera, Sukhorukova, Nadezda, Ugon, Julien

“…We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not be…”
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Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets Autor Migliorati, Giovanni

“…We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any…”
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Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points Autor Migliorati, Giovanni, Nobile, Fabio, Tempone, Raúl

“…We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise…”
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Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients Autor Nobile, F., Tempone, Raul

“…We consider the problem of numerically approximating statistical moments of the solution of a time‐dependent linear parabolic partial differential equation…”
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Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets Autor Migliorati, Giovanni, Nobile, Fabio

“…We analyze the stability and accuracy of discrete least squares on multivariate polynomial spaces to approximate a given function depending on a multivariate…”
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Discrete Least-Squares Approximations over Optimized Downward Closed Polynomial Spaces in Arbitrary Dimension Autor Cohen, Albert, Migliorati, Giovanni, Nobile, Fabio

“…We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces P Λ : = span { y ↦ y ν : ν ∈ Λ } with Λ ⊂…”
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Power Series Kernels Autor Zwicknagl, Barbara

“…We introduce a class of analytic positive definite multivariate kernels which includes infinite dot product kernels as sometimes used in machine learning,…”
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Increasing the polynomial reproduction of a quasi-interpolation operator Autor Waldron, Shayne

“…Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces…”
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Asymptotic expansions for multivariate polynomial approximation Autor Walz, Guido

“…In this paper the approximation of multivariate functions by (multivariate) Bernstein polynomials is considered. Building on recent work of Lai (J. Approx…”
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