On the Convergence of Monte Carlo–Generalized Polynomial Chaos for Uncertainty Propagation in K eff Computations for Neutronics

This paper addresses the analysis of power iteration methods applied to eigenvalue problems involving uncertainty. While several uncertain power iteration procedures based on Monte Carlo–generalized Polynomial Chaos (MC-gPC) have been proposed in the literature and have demonstrated empirical convergence, a theoretical justification of their convergence properties remains lacking. The objective of this work is to investigate the convergence behavior of such methods in a stochastic or parametric uncertainty setting. The proposed framework focuses on the propagation of uncertainty through the MC-gPC power iteration process and on the characterization of the resulting random eigenvalues and eigenfunctions. By combining spectral analysis with probabilistic tools, the study establishes conditions and assumptions in which sense convergence can be guaranteed.