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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Vydáno v:BIT (Nordisk Tidskrift for Informationsbehandling) Ročník 51; číslo 3; s. 669 - 694
Hlavní autoři: Klann, E., Ramlau, R., Reichel, L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.09.2011
Springer
Témata:
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
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Abstract 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.
AbstractList 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.
Author Reichel, L.
Klann, E.
Ramlau, R.
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Cites_doi 10.1016/j.acha.2008.02.002
10.1007/s002110050234
10.1007/BF01385512
10.1137/040605023
10.1088/0266-5611/22/1/009
10.1007/s11075-009-9282-3
10.1007/s002110050455
10.1007/s002110050379
10.1137/070694065
10.1137/1.9780898718003
10.4171/rmi/107
10.1137/S0036142997317924
10.1007/978-3-663-01409-6
10.1016/0041-5553(86)90002-9
10.1016/j.cam.2009.03.019
10.1137/1.9781611971484
10.1007/978-94-009-1740-8
10.1137/1.9781611970104
10.1023/B:BITN.0000014547.88978.05
10.1016/j.apnum.2009.07.007
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Issue 3
Keywords 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
Language English
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Snippet The representation of linear operator equations in terms of wavelet bases yields a multilevel framework, which can be exploited for iterative solution. This...
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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
Title Wavelet-based multilevel methods for linear ill-posed problems
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