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Mathematics of Computation

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Uniqueness of the optimal nodes of quadrature formulae

Author: Borislav D. Bojanov
Journal: Math. Comp. 36 (1981), 525-546
MSC: Primary 65D30; Secondary 41A55
MathSciNet review: 606511
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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}$.

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Article copyright: © Copyright 1981 American Mathematical Society

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