Estimates of linear expressions through factorization

TL;DR

This paper develops factorization techniques and generalized Taylor estimates to improve bounds on linear functionals, with applications to numerical integration rules like trapezoidal and Simpson's methods.

Contribution

It introduces new factorization results and generalized Taylor estimates for better error bounds in numerical integration.

Findings

Derived new error bounds for trapezoidal rule

Extended Taylor theorem for linear functional estimates

Applied results to Simpson's rule

Abstract

The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including applications to the trapezoidal rule as well as to a Simpson formula-type rule.