Calculation of the Norm of the Error Functional of Optimal Quadrature Formulas in the Space $W_2^{(2,1)}(0,1)$

TL;DR

This paper calculates the squared norm of the error functional for optimal quadrature formulas within the specific Sobolev space $W_2^{(2,1)}(0,1)$, providing precise error analysis.

Contribution

It provides an explicit calculation of the error functional norm for optimal quadrature formulas in the Sobolev space $W_2^{(2,1)}(0,1)$, advancing error estimation methods.

Findings

Explicit formula for the squared norm of the error functional.

Enhanced understanding of quadrature error in $W_2^{(2,1)}(0,1)$.

Potential applications in numerical integration accuracy assessment.

Abstract

In this paper in the space $W_2^{(2,1)}(0,1)$ square of the norm of the error functional of a optimal quadrature formula is calculated.