ISSN:
1572-9125
Keywords:
41A55
;
65D32
;
quadrature formulas
;
compound Newton-Cotes quadrature formulas
;
piecewise polynomial interpolation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider quadrature formulas defined by piecewise polynomial interpolation at equidistant nodes, admitting the nodes of adjacent polynomials to overlap, which generalizes the interpolation scheme of the compound Newton-Cotes quadrature formulas. The error constantse μ,n in the estimate $$|R_n [f]| \leqslant e_{\mu ,n} ||f^{(\mu )} ||_\infty$$ are considered for the highest possible values of μ, which are μ=r ifr is even, and μ=r+1 ifr is odd (wherer − 1 is the degree of the polynomials used for interpolation). It is determined which quadrature formulas of the type introduced have (asymptotically) the least error constant. As a result, though the compound Newton-Cotes quadrature formulas have an optimality property, they are not the best formulas of this type.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01933266
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