A Complement Proposal for Optimization of Subgroup Parameters

Abstract

A new theory and methodology to optimize subgroup parameters were established by the use of Chebyshev approximation. The optimization of the fitting method was realized by the minimax approximation provided by the Remes algorithm. As for the moment method, a new definition for moments was proposed to cure the poor reproducibility of effective cross section by the original moment method. The new moment method uses transformed Chebyshev polynomials as orthogonal bases. This method is mathematically stable and the efficiency was verified by a numerical example. It was also shown that use of preconditioning can furthermore enhance the efficiency. The first dominant term of the new moments can be approximated by old moment definition σα with α= 0.1–0:6, including the case with α=−1/2. This fact can explain the efficiency of the reservation of half-integer moments in the reproducibility of effective cross section that was mentioned by Unesaki.

KEYWORDS:

• subgroup parameters
• fitting method
• moment method
• Chebyshev approximation
• minimax approximation
• Remes algorithm
• half integer moment
• effective cross section