Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1499–1519

A new unbiased stochastic algorithm for solving linear Fredholm equations of the second kind

Article

Abstract

In this paper, we propose and analyse a new unbiased stochastic approach for solving a class of integral equations. We study and compare the proposed unbiased approach against the known biased Monte Carlo method based on evaluation of truncated Liouville-Neumann series. We also compare the proposed algorithm against the deterministic Nystrom method. Extensions of the unbiased method for the weak and global solutions are described. Extensive numerical experiments have been performed to support the theoretical studies regarding the convergence of the unbiased algorithms. The results are compared to the best known biased Monte Carlo algorithms for numerical integration done in our previous studies. Conclusions about the applicability and efficiency of the proposed algorithms have been drawn.

Keywords

Integral equations Algorithm Unbiased approach

Mathematics Subject Classification (2010)

45Bxx 65Bxx 65Cxx 65Rxx

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Authors and Affiliations

• I. T. Dimov
• 1
• S. Maire
• 2
1. 1.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria
2. 2.Laboratoire LIS, UMR 7020 Equipe Signal et ImageSeaTech - Université de ToulonLa GardeFrance

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