Constructing Least-Squares Polynomial Approximations (Q5113170)

scientific article; zbMATH DE number 7207348

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English	Constructing Least-Squares Polynomial Approximations	scientific article; zbMATH DE number 7207348

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instance of

scholarly article

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title

Constructing Least-Squares Polynomial Approximations (English)

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3 June 2020

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zbMATH Keywords

least-squares approximations

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polynomial approximations

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optimal sampling

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describes a project that uses

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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

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Universal algorithms for learning theory. II: Piecewise polynomial functions

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Q3546378

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Weighted pluripotential theory in C N

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Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points

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Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory

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Q3690890

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Uniform approximation by discrete least squares polynomials

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Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

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High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs

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Polynomial approximation via compressed sensing of high-dimensional functions on lower sets

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On the stability and accuracy of least squares approximations

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Convergence rates of best $N$-term Galerkin approximations for a class of elliptic SPDEs

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Optimal weighted least-squares methods

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Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

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Q4820343

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A set of orthogonal polynomials induced by a given orthogonal polynomial

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Data-driven polynomial chaos expansions: a weighted least-square approximation

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Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation

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A gradient enhanced $\ell_{1}$-minimization for sparse approximation of polynomial chaos expansions

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A distribution-free theory of nonparametric regression

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Least squares polynomial chaos expansion: a review of sampling strategies

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Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies

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Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression

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Monte Carlo and quasi-Monte Carlo sampling

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Adaptive Polynomial Approximation by Means of Random Discrete Least Squares

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Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

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Approximation of quantities of interest in stochastic PDEs by the random discrete $L^2$ projection on polynomial spaces

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Computation of induced orthogonal polynomial distributions

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Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation

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A Christoffel function weighted least squares algorithm for collocation approximations

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Stochastic Collocation on Unstructured Multivariate Meshes

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Sequential function approximation with noisy data

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Nonadaptive quasi-optimal points selection for least squares linear regression

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A randomized Kaczmarz algorithm with exponential convergence

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Multivariate polynomial approximation in the hypercube

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User-friendly tail bounds for sums of random matrices

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The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

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A Gradient-Enhanced L1 Approach for the Recovery of Sparse Trigonometric Polynomials

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STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION

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full work available at URL

https://doi.org/10.1137/18m1234151

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Identifiers

zbMATH Open document ID

1450.41001

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DOI

10.1137/18M1234151

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:5113170