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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| Published in: | Numerical functional analysis and optimization Vol. 19; no. 3-4; pp. 353 - 375 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia, PA
Marcel Dekker, Inc
01.01.1998
Taylor & Francis |
| Subjects: | |
| ISSN: | 0163-0563, 1532-2467 |
| Online Access: | Get full text |
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| Abstract | 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 |
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| AbstractList | 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 |
| Author | Scherzer, Otmar Strohmer, Thomas |
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| Cites_doi | 10.1111/j.1365-246X.1968.tb00216.x 10.1007/s002110050158 10.1093/oso/9780198596998.001.0001 10.1007/BF01385781 10.1088/0266-5611/10/3/018 10.1006/acha.1996.0007 10.1016/B978-0-12-174590-5.50020-4 10.1007/978-94-009-1740-8 10.1007/978-94-009-3713-0 10.1016/0024-3795(93)90275-S 10.1007/BF02570568 10.1007/s002110050101 |
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| Issue | 3-4 |
| Keywords | 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 |
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| References | Backus G. (CIT0001) 1968; 16 Istratescu V.I. (CIT0015) 1987 Rauth M. (CIT0019) 1988 Hanke M. (CIT0013) 1995 CIT0012 Young R. (CIT0021) 1980 CIT0011 CIT0022 Mallat S. (CIT0017) 1989; 315 Zayed A.I. (CIT0023) 1993 Groetsch C.W. (CIT0010) 1984 Saitho S. (CIT0020) Gröchenig K.H (CIT0007) 1994 Benedetto J. (CIT0002) 1992 Benedetto J. (CIT0003) 1992 CIT0005 CIT0016 CIT0004 Higgins J.R. (CIT0014) 1996 CIT0018 CIT0006 CIT0009 CIT0008 |
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| SubjectTerms | 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 |
| Title | A multi-level algorithm for the solution of moment problems |
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