Wavelet-based multilevel methods for linear ill-posed problems

The representation of linear operator equations in terms of wavelet bases yields a multilevel framework, which can be exploited for iterative solution. This paper describes cascadic multilevel methods that employ conjugate gradient-type methods on each level. The iterations are on each level termina...

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Bibliographic Details
Published in:BIT (Nordisk Tidskrift for Informationsbehandling) Vol. 51; no. 3; pp. 669 - 694
Main Authors: Klann, E., Ramlau, R., Reichel, L.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.09.2011
Springer
Subjects:
Computational Mathematics and Numerical Analysis
Exact sciences and technology
Fourier analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Wavelet
65R32
65R30
Multilevel method
Ill-posed problem
Minimal residual method
65T60
65N55
Conjugate gradient method
Operator equation
Numerical linear algebra
Iterative method
Iteration
Linear operator
Regularization method
Wavelets
Numerical analysis
Wavelet transformation
Ill posed problem
ISSN:0006-3835, 1572-9125
Online Access:Get full text
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Summary:The representation of linear operator equations in terms of wavelet bases yields a multilevel framework, which can be exploited for iterative solution. This paper describes cascadic multilevel methods that employ conjugate gradient-type methods on each level. The iterations are on each level terminated by a stopping rule based on the discrepancy principle.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-011-0320-x