Fast algorithms for computing defects and their derivatives in the Regge calculus

TL;DR

This paper presents an efficient algorithm for computing defect angles and their derivatives in Regge calculus, facilitating the solution of large non-linear systems using Newton-Raphson methods.

Contribution

It introduces a novel algorithm specifically designed for fast computation of defects and derivatives in Regge calculus, improving numerical efficiency.

Findings

Algorithm significantly reduces computation time.

Enables practical solutions to large Regge systems.

Improves accuracy of defect and derivative calculations.

Abstract

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg-lengths. The purpose of this paper is to present details of such an algorithm.