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. 
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References

The theory of splines and their applications
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