BEST QUADRATURE FORMULAS FOR CLASSES OF DIFFERENTIABLE FUNCTIONS AND PIECEWISE-POLYNOMIAL APPROXIMATION

@article{Korneiuk1969BESTQF,
title={BEST QUADRATURE FORMULAS FOR CLASSES OF DIFFERENTIABLE FUNCTIONS AND PIECEWISE-POLYNOMIAL APPROXIMATION},
author={N. Kornei{\vc}uk and N. E. Lu{\vs}paĭ},
journal={Mathematics of The Ussr-izvestiya},
year={1969},
volume={3},
pages={1335-1355}
}

In this article we obtain characteristic properties of piecewise-polynomial functions (spline functions) that have least deviation from zero in the metric of C. This has allowed us to obtain quadrature formulas with least estimate of the remainder on a number of classes of differentiable functions.