A finite-precision Lanczos-Golub-Welsch route to probability-table construction in resonance self-shielding

TL;DR

This paper introduces a finite-precision method for constructing probability tables in resonance self-shielding, replacing traditional pipelines with a Lanczos-Golub-Welsch approach that improves accuracy and stability.

Contribution

It reformulates the problem as a polynomial-moment problem and develops an alternative construction route using discrete measures, Lanczos reduction, and Golub-Welsch extraction.

Findings

Lower effective-cross-section errors in tested cases

Avoids complex responses caused by order effects

Preserves nonnegative-realness during compression

Abstract

This work reformulates Chiba's affine-order prescription as a polynomial-moment problem for a transformed positive measure, and develops an alternative finite-precision construction route based on this reformulation. The proposed construction proceeds through discrete-measure realization, symmetric Lanczos reduction, and Golub--Welsch extraction, replacing the conventional moment--Pade pipeline. The subgroup total levels and probabilities are obtained by a Gauss-type compression step that preserves nonnegative-realness, while the reaction-channel levels are recovered on the compressed nodes by orthogonal-basis matching. In five tested resonance-channel cases, the proposed construction yields lower effective-cross-section errors and avoids the order-induced emergence of complex responses observed in the conventional construction.