Wavelet approximation in weighted Sobolev spaces of mixed order with applications to the electronic Schrödinger equation

DOI10.1007/s00365-011-9138-7zbMath1253.41016OpenAlexW2082597397MaRDI QIDQ431155

Andreas Zeiser

Publication date: 26 June 2012

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

Full work available at URL: https://doi.org/10.1007/s00365-011-9138-7

zbMATH Keywords

weighted Sobolev spacessparse gridsapproximation spacesbiorthogonal waveletsnorm equivalenceshyperbolic cross

Mathematics Subject Classification ID

Numerical methods for wavelets (65T60) Rate of convergence, degree of approximation (41A25) Applications to the sciences (65Z05) Molecular physics (81V55) Approximation by other special function classes (41A30)

Related Items

A note on the construction of \(L\)-fold sparse tensor product spaces ⋮ The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces ⋮ An Adaptive Multiscale Approach for Electronic Structure Methods ⋮ Estimation of linear operators from scattered impulse responses ⋮ Regularity, Complexity, and Approximability of Electronic Wavefunctions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast matrix-vector multiplication in the sparse-grid Galerkin method
• An adaptive wavelet method for solving high-dimensional elliptic PDEs
• Regularity and approximability of electronic wave functions
• Wavelet bases in the weighted Besov and Triebel-Lizorkin spaces with \(A_p^{\text{loc}}\)-weights
• Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross
• Hyperbolic wavelet approximation
• Optimized tensor-product approximation spaces
• d-Variate Boolean interpolation
• A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives
• On \(N\) -termed approximations in \(H^s\)-norms with respect to the Haar system
• The mixed regularity of electronic wave functions multiplied by explicit correlation factors
• Optimized general sparse grid approximation spaces for operator equations
• Orthonormal bases of compactly supported wavelets
• Ten Lectures on Wavelets
• On Compactly Supported Spline Wavelets and a Duality Principle
• Biorthogonal bases of compactly supported wavelets
• Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
• Function Spaces with Exponential Weights I
• Adaptive wavelet methods for elliptic operator equations: Convergence rates
• Intertwining Multiresolution Analyses and the Construction of Piecewise-Polynomial Wavelets
• Sparse grids
• Adaptive wavelet algorithms for elliptic PDE's on product domains
• On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique

This page was built for publication: Wavelet approximation in weighted Sobolev spaces of mixed order with applications to the electronic Schrödinger equation