Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30, 41A55

Retrieve articles in all journals with MSC: 65D30, 41A55


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0606511-4
PII: S 0025-5718(1981)0606511-4
Article copyright: © Copyright 1981 American Mathematical Society