A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions
From MaRDI portal
Publication:2007287
DOI10.1016/j.camwa.2015.12.045zbMath1443.65010arXiv1508.01125OpenAlexW2963940996MaRDI QIDQ2007287
Clayton G. Webster, Miroslav K. Stoyanov
Publication date: 12 October 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1508.01125
Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)
Related Items (5)
A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions ⋮ A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs ⋮ An Evolve-Filter-Relax Stabilized Reduced Order Stochastic Collocation Method for the Time-Dependent Navier--Stokes Equations ⋮ Numerical analysis of a second order ensemble algorithm for numerical approximation of stochastic Stokes-Darcy equations ⋮ The Gap between Theory and Practice in Function Approximation with Deep Neural Networks
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients
- High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
- A non-adapted sparse approximation of PDEs with stochastic inputs
- Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
- A method for numerical integration on an automatic computer
- A least-squares approximation of partial differential equations with high-dimensional random inputs
- On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection
- Simple cubature formulas with high polynomial exactness
- Greedy algorithms for reduced bases in Banach spaces
- A general multipurpose interpolation procedure: The magic points
- On Leja sequences: some results and applications
- Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
- ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods
- Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Stochastic finite element methods for partial differential equations with random input data
- A GRADIENT-BASED SAMPLING APPROACH FOR DIMENSION REDUCTION OF PARTIAL DIFFERENTIAL EQUATIONS WITH STOCHASTIC COEFFICIENTS
- Sparse grids
This page was built for publication: A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions