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Finite moment problems and applications to multiphase computations in geometric optics
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-6321-8619
2005 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 3, no 3, 373-392 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2005. Vol. 3, no 3, 373-392 p.
Keyword [en]
moment problem, Vlasov equation, nonstrictly hyperbolic systems, geometric optics, scalar conservation-laws, schrodinger-type equations, hamilton-jacobi equations, semiclassical limit, entropy solutions, maximum-entropy, approximations, singularities, dynamics, systems
URN: urn:nbn:se:kth:diva-15325ISI: 000235557600005OAI: diva2:333366
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Runborg, Olof
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