Mathematical Resolution of Ill-Posedness in Padé-Based Subgroup Parameter Calculation via Regularization and Pole–Residue Constraints

Abstract

The Padé-based method for subgroup parameter calculation in resonance self-shielding analysis is ill-posed: the truncated overdetermined system, the Vandermonde-type coefficient matrix, and the unenforced pole–residue structure jointly produce unstable poles and subgroup parameters that violate non-negativity or the probability normalization. This paper proposes the regularized overdetermined Padé approximation (ROPA), a two-stage, structure-preserving procedure that resolves this ill-posedness at the level of the mathematical problem rather than the numerical workflow. In stage one, the overdetermined least-squares Padé system is built on a normalized background cross-section variable with column equilibration and Tikhonov regularization, the poles are computed as eigenvalues of a companion matrix, and a reflection gate maps them onto the positive real axis. In stage two, the subgroup probabilities are recovered by a convex quadratic program enforcing non-negativity and unit sum, with non-negative least squares for partial probability channels. The well-posedness of the regularized problem is established theoretically, including an explicit stability bound with respect to perturbations of the resonance integral data. Validation against OpenMC Monte Carlo references on ENDF/B-VIII.0 data for 235U, 238U, and 240Pu over 16 resonance groups, together with VERA pin-cell and lattice benchmarks, demonstrates that ROPA achieves accuracy comparable to or higher than existing methods while guaranteeing admissible parameters in all tested cases.