Communications in Mathematical Sciences

Volume 3 (2005)

Number 3

Finite Moment Problems and Applications to Multiphase Computations in Geometric Optics

Pages: 373 – 392

DOI: http://dx.doi.org/10.4310/CMS.2005.v3.n3.a5

Authors

Laurent Gosse

Olof Runborg

Abstract

Recovering a function out of a finite number of moments is generally an ill-posed inverse problem. We focus on two special cases arising from applications to multiphase geometric optics computations where this problem can be carried out in a restricted class of given densities. More precisely, we present a simple algorithm for the inversion of Markov's moment problem which appears in the treatment of Brenier and Corrias' "K-multibranch solutions" and study Stieltje's algorithm in order to process moment systems arising from a Wigner analysis. Numerical results are provided for moderately intricate wave-fields.

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