A Quasi Monte Carlo Method for Large-Scale Inverse Problems

Nick Polydorides, Mengdi Wang, Dimitri P. Bertsekas

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We consider large-scale linear inverse problems with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we implement importance sampling schemes, specially tailored to the structure of inverse problems. We emphasize various alternative methods for approximating the optimal sampling distribution and we demonstrate their impact on the reduction of simulation noise. The performance of our algorithm is tested on a practical inverse problem arising from Fredholm integral equations of the first kind.

Original languageEnglish (US)
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2010
PublisherSpringer New York LLC
Pages623-637
Number of pages15
ISBN (Print)9783642274398
DOIs
StatePublished - 2012
Event9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, Poland
Duration: Aug 15 2010Aug 20 2010

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume23
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
CountryPoland
CityWarsaw
Period8/15/108/20/10

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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