Uniqueness of the optimal nodes of quadrature formulae

Author:
Borislav D. Bojanov

Journal:
Math. Comp. **36** (1981), 525-546

MSC:
Primary 65D30; Secondary 41A55

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606511-4

MathSciNet review:
606511

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Abstract: We prove the uniqueness of the quadrature formula with minimal error in the space , of -periodic differentiable functions among all quadratures with *n* free nodes , , of fixed multiplicities , respectively. As a corollary, we get that the equidistant nodes are optimal in for if .

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0606511-4

Article copyright:
© Copyright 1981
American Mathematical Society