Adaptive frame methods for elliptic operator equations

DOI10.1007/s10444-005-7501-6zbMath1122.65103OpenAlexW1978139958MaRDI QIDQ996791

Stephan Dahlke, Massimo Fornasier, Thorsten Raasch

Publication date: 19 July 2007

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-005-7501-6

zbMATH Keywords

convergencedomain decompositionsparse matricesBanach framesnorm equivalencesmultiscale methodsoverdetermined systemsadaptive frame algorithmelliptic operator equationsGelfand framesGelfand wavelet frames

Mathematics Subject Classification ID

Related Items (43)

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Cites Work

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• Banach spaces related to integrable group representations and their atomic decompositions. I
• Stable multiscale bases and local error estimation for elliptic problems
• A discrete transform and decompositions of distribution spaces
• Intrinsic localization of frames
• Adaptive frame methods for elliptic operator equations
• Describing functions: Atomic decompositions versus frames
• Multilevel preconditioning
• Wavelets with complementary boundary conditions -- functions spaces on the cube
• Biorthogonal spline wavelets on the interval -- stability and moment conditions
• A posteriori error estimation and adaptive mesh-refinement techniques
• Gabor analysis and algorithms. Theory and applications
• Quasi-orthogonal decompositions of structured frames.
• Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order
• Localization of frames. II
• Advances in Gabor analysis
• Adaptive wavelet methods. II: Beyond the elliptic case
• Pseudodifferential operators on \(\alpha\)-modulation spaces.
• Localization of frames, Banach frames, and the invertibility of the frame operator
• Adaptive error control for multigrid finite element methods
• Approximation of the inverse frame operator and applications to Gabor frames
• Finite-dimensional approximation of the inverse frame operator
• Weighted coorbit spaces and Banach frames on homogeneous spaces
• Flexible Gabor-wavelet atomic decompositions for \(L^2\) -Sobolev spaces
• Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments
• Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• Iterative Reconstruction of Multivariate Band-Limited Functions from Irregular Sampling Values
• Ten Lectures on Wavelets
• A‐posteriori error estimates for the finite element method
• Composite wavelet bases for operator equations
• Adaptive Solution of Operator Equations Using Wavelet Frames
• Adaptive wavelet methods for elliptic operator equations: Convergence rates
• Adaptive wavelet methods for saddle point problems
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• Adaptive Wavelet Methods for Saddle Point Problems---Optimal Convergence Rates
• A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions
• Wavelets on Manifolds I: Construction and Domain Decomposition
• Nonlinear approximation in α ‐modulation spaces
• An introduction to frames and Riesz bases

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