Department of Mathematics
A multi-level algorithm for the solution of moment problems
- Author(s): Scherzer, Otmar
- Strohmer, Thomas
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/9901121.pdf
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.