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A multi-level algorithm for the solution of moment problems

Otmar Scherzer·Thomas Strohmer
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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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Otmar Scherzer, Thomas Strohmer. 1999-01-26. A multi-level algorithm for the solution of moment problems. https://arxiv.org/abs/math/9901121

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