Least-squares fitting applied to nuclear mass formulas. Resolution by the Gauss-Seidel method

TL;DR

This paper presents a simple, efficient numerical method using least-squares fitting and Gauss-Seidel iterations to optimize nuclear mass formulas, capable of handling large datasets quickly and effectively.

Contribution

It introduces a practical iterative approach for least-squares optimization of nuclear mass formulas using Gauss-Seidel, suitable for large and symmetric positive-definite systems.

Findings

Method is simple to implement and fast.

Applicable to large datasets and similar linear systems.

Effective for optimizing nuclear mass formulas.

Abstract

A numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss-Seidel scheme. The steps of the algorithm are given in detail. In practice the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.