A Primal-dual algorithm for unfolding neutron energy spectrum from multiple activation foils

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^{m\times 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.