Computational scales of Sobolev norms with application to preconditioning

DOI10.1090/S0025-5718-99-01106-0zbMath0941.65052MaRDI QIDQ4942774

James H. Bramble, Panayot S. Vassilevski, Joseph E. Pasciak

Publication date: 15 March 2000

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Hilbert spacedomain decompositionTikhonov regularizationpseudo-differential operatorsSobolev normsmultilevel preconditioners

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Boundary value problems for PDEs with pseudodifferential operators (35S15) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

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Cites Work

• A robust hierarchical basis preconditioner on general meshes
• Local decomposition of refinable spaces and wavelets
• Parallel Multilevel Preconditioners
• Iterative Schemes for Nonsymmetric and Indefinite Elliptic Boundary Value Problems
• Error bounds for tikhonov regularization in hilbert scales
• Error Estimates for Regularization Methods in Hilbert Scales
• New Estimates for Multilevel Algorithms Including the V-Cycle
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