Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation
From MaRDI portal
Publication:4603503
DOI10.1137/17M1140960zbMath1382.41005arXiv1708.01296OpenAlexW2745187354MaRDI QIDQ4603503
Liang Yan, Ling Guo, Tao Zhou, Akil C. Narayan
Publication date: 21 February 2018
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.01296
Related Items
Optimal design for kernel interpolation: applications to uncertainty quantification ⋮ Boosted optimal weighted least-squares ⋮ Polynomial chaos expansions for dependent random variables ⋮ Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data ⋮ Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification ⋮ A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs ⋮ A gradient enhanced \(\ell_{1}\)-minimization for sparse approximation of polynomial chaos expansions ⋮ Constructing Least-Squares Polynomial Approximations ⋮ Data-driven polynomial chaos expansions: a weighted least-square approximation ⋮ Weighted Fekete points on the real line and the unit circle ⋮ A Reduced-Basis Polynomial-Chaos Approach with a Multi-parametric Truncation Scheme for Problems with Uncertainties ⋮ On the stability and accuracy of the empirical interpolation method and gravitational wave surrogates
Cites Work
- 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
- A non-adapted sparse approximation of PDEs with stochastic inputs
- On the calculation of approximate fekete points: the univariate case
- Uniform approximation by discrete least squares polynomials
- Computing approximate Fekete points by QR factorizations of Vandermonde matrices
- Computation of induced orthogonal polynomial distributions
- Generation and application of multivariate polynomial quadrature rules
- Weighted discrete least-squares polynomial approximation using randomized quadratures
- Sparse grid collocation schemes for stochastic natural convection problems
- A class of orthogonal polynomials
- Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression
- Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces
- Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation
- On Sparse Interpolation and the Design of Deterministic Interpolation Points
- On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification
- A Christoffel function weighted least squares algorithm for collocation approximations
- Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
- Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points
- An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- Optimal weighted least-squares methods
- Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation
- Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
- A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions
- Minimizing the Condition Number to Construct Design Points for Polynomial Regression Models
- Stochastic Collocation on Unstructured Multivariate Meshes
- STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION
- High-Order Collocation Methods for Differential Equations with Random Inputs
