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- W3023807306 abstract "In this paper we propose a robust and efficient primal-dual interior-point method for a nonlinear ill-conditioned problem with associated errors which are arising in the unfolding procedure for neutron energy spectrum from multiple activation foils. Based on the maximum entropy principle and Boltzmann's entropy formula, the discrete form of the unfolding problem is equivalent to computing the analytic center of the polyhedral set begin{document}$ P = {x in R^n mid Ax = b, x ge 0} $end{document} , where the matrix begin{document}$ A in R^{mtimes n} $end{document} is ill-conditioned, and both begin{document}$ A $end{document} and begin{document}$ b $end{document} are inaccurate. By some derivations, we find a new regularization method to reformulate the problem into a well-conditioned problem which can also reduce the impact of errors in begin{document}$ A $end{document} and begin{document}$ b $end{document} . Then based on the primal-dual interior-point methods for linear programming, we propose a hybrid algorithm for this ill-conditioned problem with errors. Numerical results on a set of ill-conditioned problems for academic purposes and two practical data sets for unfolding the neutron energy spectrum are presented to demonstrate the effectiveness and robustness of the proposed method." @default.
- W3023807306 created "2020-05-13" @default.
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- W3023807306 date "2021-01-01" @default.
- W3023807306 modified "2023-09-23" @default.
- W3023807306 title "A Primal-dual algorithm for unfolding neutron energy spectrum from multiple activation foils" @default.
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- W3023807306 doi "https://doi.org/10.3934/jimo.2020073" @default.
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