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An approximation of the surfaces areas using the classical Bernstein quadrature formula
Author(s) -
Miclăuş Dan
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5346
Subject(s) - mathematics , quadrature (astronomy) , bernstein polynomial , clenshaw–curtis quadrature , gauss–kronrod quadrature formula , function approximation , numerical approximation , adaptive quadrature , numerical integration , spouge's approximation , tanh sinh quadrature , mathematical analysis , approximation error , gaussian quadrature , numerical analysis , integral equation , nyström method , computer science , artificial neural network , artificial intelligence , control (management) , electrical engineering , control theory (sociology) , engineering
In this article, we try to assign a place on the map of the closed Newton–Cotés quadrature formulas to a new approximation formula based on the classical Bernstein polynomials. We create a procedure for a computer implementation that allows us to verify the accuracy of the new approximation formula. In order to get a complete image of this kind of approximation, we compare some well‐known quadrature formulas. Although effective in most situations, there are instances when the composite quadrature formulas cannot be applied, as they use equally‐spaced nodes. We present also an adaptive method that is used to obtain better approximations and to minimize the number of function evaluations. Numerical examples are given to increase the validity of the theoretical aspects.