A note on the construction of \(L\)-fold sparse tensor product spaces

DOI10.1007/s00365-012-9178-7zbMath1283.41015OpenAlexW2026461371MaRDI QIDQ378147

Michael Griebel, Helmut Harbrecht

Publication date: 11 November 2013

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-012-9178-7

zbMATH Keywords

sparse gridshigh-dimensional problemsoptimal construction of sparse gridsrate of approximationsparse tensor product of ansatz spaces with different approximation powersparse tensor product spacestensor product domains of different dimensions

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25) Approximation by other special function classes (41A30)

Related Items

Stable splittings of Hilbert spaces of functions of infinitely many variables, Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness, On tensor product approximation of analytic functions, Analysis of tensor approximation schemes for continuous functions, B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness, Space-time Multilevel Quadrature Methods and their Application for Cardiac Electrophysiology, Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs, Sparse approximation of multilinear problems with applications to kernel-based methods in UQ, Sampling and cubature on sparse grids based on a B-spline quasi-interpolation, Hyperbolic cross approximation in infinite dimensions, A sparse-grid isogeometric solver, Fast Discrete Fourier Transform on Generalized Sparse Grids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Combination technique based \(k\)-th moment analysis of elliptic problems with random diffusion
• Wavelet approximation in weighted Sobolev spaces of mixed order with applications to the electronic Schrödinger equation
• Sparse second moment analysis for elliptic problems in stochastic domains
• Sparse adaptive finite elements for radiative transfer
• Sparse finite elements for stochastic elliptic problems --- higher order moments
• Sparse finite elements for elliptic problems with stochastic loading
• Sparse grids for boundary integral equations
• Continuous algorithms in \(n\)-term approximation and nonlinear widths
• A sparse grid space-time discretization scheme for parabolic problems
• Sparse grid spaces for the numerical solution of the electronic Schrödinger equation
• The Periodic Unfolding Method in Domains with Holes
• Space-time adaptive wavelet methods for parabolic evolution problems
• Optimized general sparse grid approximation spaces for operator equations
• Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results
• Multiscale Modelling of Complex Fluids: A Mathematical Initiation
• High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales
• Multiscale convergence and reiterated homogenisation
• On the construction of sparse tensor product spaces
• The Periodic Unfolding Method in Homogenization
• Space-Time Approximation with Sparse Grids