A multi-level algorithm for the solution of moment problems

We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the Landweber-Richardson method are proposed that determine the "optim...

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Bibliographic Details
Published in:Numerical functional analysis and optimization Vol. 19; no. 3-4; pp. 353 - 375
Main Authors: Scherzer, Otmar, Strohmer, Thomas
Format: Journal Article
Language:English
Published: Philadelphia, PA Marcel Dekker, Inc 01.01.1998
Taylor & Francis
Subjects:
AMS Subject Classification 42A15
AMS Subject Classification 62D05
AMS Subject Classification 65J10
AMS Subject Classification 65J20
AMS Subject Classification: 44A60
conjugate gradient method
Exact sciences and technology
Fourier analysis
Integral transforms, operational calculus
Landweber Richardson method
Mathematical analysis
Mathematics
Moment problems
multi-level algorithms
nonuniform sampling
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Probability and statistics
Sampling theory, sample surveys
Sciences and techniques of general use
Statistics
Conjugate gradient method
Stability
Sobolev space
Reproducing kernel Hilbert space (rkHis)
Landweber Richardson method
Moment problem
Hilbert space
Signal recovery
Band limited signal
Algorithm
Multi level algorithm (mla)
Convergence
ISSN:0163-0563, 1532-2467
Online Access:Get full text
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Summary:We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the Landweber-Richardson method are proposed that determine the "optimal" reconstruction level a posteriori from quantities that arise during the numerical calculations. As an important example we discuss the reconstruction of band-limited signals from irregularly spaced noisy samples, when the actual bandwidth of the signal is not available. Numerical examples show the usefulness of the proposed algorithms
ISSN:0163-0563
1532-2467
DOI:10.1080/01630569808816833