Uniqueness of the optimal nodes of quadrature formulae
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- by Borislav D. Bojanov PDF
- Math. Comp. 36 (1981), 525-546 Request permission
Abstract:
We prove the uniqueness of the quadrature formula with minimal error in the space $\tilde W_q^r[a,b],1 < q < \infty$, of $(b - a)$-periodic differentiable functions among all quadratures with n free nodes $\{ {x_k}\} _1^n$, $a = {x_1} < \cdots < {x_n} < b$, of fixed multiplicities $\{ {v_k}\} _1^n$, respectively. As a corollary, we get that the equidistant nodes are optimal in $\tilde W_q^r[a,b]$ for $1 \leqslant q \leqslant \infty$ if ${v_1} = \cdots = {v_n}$.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- 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