Multivariate Approximation in Downward Closed Polynomial Spaces

DOI10.1007/978-3-319-72456-0_12zbMath1405.41021arXiv1612.06690OpenAlexW2581598540MaRDI QIDQ4611802

Albert Cohen, Giovanni Migliorati

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.06690

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximation by polynomials (41A10) Algorithms for approximation of functions (65D15)

Related Items

An Adaptive Sampling and Domain Learning Strategy for Multivariate Function Approximation on Unknown Domains, Near-optimal approximation methods for elliptic PDEs with lognormal coefficients, On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion, A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property, Polynomial approximation of anisotropic analytic functions of several variables, Sparse polynomial approximations for affine parametric saddle point problems, Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces, On the cardinality of lower sets and universal discretization, Uncertainty Quantification for Low-Frequency, Time-Harmonic Maxwell Equations with Stochastic Conductivity Models, Towards optimal sampling for learning sparse approximation in high dimensions, Pluripotential numerics, Reduced Basis Greedy Selection Using Random Training Sets, Compressive Hermite interpolation: sparse, high-dimensional approximation from gradient-augmented measurements, Adaptive Approximation by Optimal Weighted Least-Squares Methods, Nonlinear methods for model reduction, Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies
• On the stability and accuracy of least squares approximations
• High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
• Analysis of discrete \(L^2\) projection on polynomial spaces with random evaluations
• Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets
• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• On the Lebesgue constant of Leja sequences for the unit disk and its applications to multivariate interpolation
• Tractability of multivariate problems. Volume III: Standard information for operators
• Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Solvability problems of bivariate interpolation I
• Deterministic and stochastic error bounds in numerical analysis
• Dimension-adaptive tensor-product quadrature
• Optimal Monte Carlo methods for \(L^2\)-approximation
• Optimal nonlinear approximation
• On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
• Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension
• On the Stability of Polynomial Interpolation Using Hierarchical Sampling
• Inverse problems: A Bayesian perspective
• Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
• Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients
• A Christoffel function weighted least squares algorithm for collocation approximations
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• The power of standard information for multivariate approximation in the randomized setting
• Spectral Methods for Uncertainty Quantification
• Computational Aspects of Polynomial Interpolation in Several Variables
• Inverse Problem Theory and Methods for Model Parameter Estimation
• Optimal weighted least-squares methods
• Approximation of high-dimensional parametric PDEs
• Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
• Adaptive Polynomial Approximation by Means of Random Discrete Least Squares
• On the power of function values for the approximation problem in various settings
• N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS