# An Optimal Quadrature Formula with Derivative in a Hilbert Space

## An Optimal Quadrature Formula with Derivative in a Hilbert Space

## Abstract

This article presents the derivation and analysis of a weighted optimal quadrature formula in the

Hilbert space

(2,1)

2 W (0,1)

. The quadrature formula is expressed as a linear combination of function values

and their first-order derivatives at equidistant nodes in the interval

[0,1]

.The coefficients are determined

by minimizing the norm of the error functional in the dual space

(2,1)*

2 W (0,1)

, which measures the

difference between the integral of a function over the interval and the quadrature approximation. Key

results include explicit expressions for the coefficients and the norm of the error functional

## References

Kh. M. Shadimetov, Optimal lattice quadrature and cubature formulas in Sobolev spaces. (T.: Fan va texnologiya, 2019) p. 224.

## Published

2024-06-07

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/507

## Issue

## Section

Computational and discrete mathematics