A recurrence scheme for least-square optimized polynomials

TL;DR

This paper introduces a recurrence method for efficiently computing high-degree polynomial approximations, exemplified by polynomials used in fermion simulation algorithms, with a practical C implementation provided.

Contribution

It presents a novel recurrence scheme for high-degree polynomial approximation and offers a practical C code for applications in fermion simulation algorithms.

Findings

Efficient computation of high-degree polynomials near zero.

Application to polynomials in the two-step multi-boson algorithm.

Code implementation supports polynomial degrees of several thousands.

Abstract

A recurrence scheme is defined for the numerical determination of high degree polynomial approximations to functions as, for instance, inverse powers near zero. As an example, polynomials needed in the two-step multi-boson (TSMB) algorithm for fermion simulations are considered. For the polynomials needed in TSMB a code in C is provided which is easily applicable to polynomial degrees of several thousands.