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Noninterpolatory Quadrature Formulas
SIAM Journal on Numerical Analysis, 1972There are infinitely many formulas of the form \[\int_{ - 1}^1 {f(x)dx = a_{ - 1} f( - 1) + a_0 f(0) + a_1 (1) + b_{ - 1} f''( - 1)b_1 f''(1)} \] that are exact for quintic polynomials, although, in general, there is no interpolating quintic through the six pieces of data. On the other hand, there is no corresponding formula for \[\int_{0}^1 {f(x)dx} \]
Epstein, M. P., Hamming, R. W.
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On the Convergence of Quadrature Formulas
SIAM Journal on Numerical Analysis, 1971Two fundamental theorems concerning quadratures are given here. The first theorem gives a constructive criterion for determining if a quadrature formula is convergent in the space of continuous functions on $[0,1]$ with maximum norm. The second theorem simply shows that Gregory’s method is convergent in the space of bounded Riemann integrable functions
Espinosa-Maldonado, Ruben J. +1 more
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Доклады Академии наук, 2018
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Russian Academy of Sciences. Izvestiya Mathematics, 1995
See the review in Zbl 0836.41020.
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See the review in Zbl 0836.41020.
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ON THE ČEBYŠEV QUADRATURE FORMULA
Mathematics of the USSR-Izvestiya, 1969In this paper we examine several weight functions for which the Cebysev quadrature formula is valid. A method is given in the general case by means of which the degree of precision of the formula may be estimated.
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On chebyshev quadrature and variance of quadrature formulas
BIT, 1988The purpose of this note is to give an example which demonstrates that one can achieve much higher algebraic precision with a quadrature rule with small but not minimal variance than with a Chebyshev rule with minimal variance.
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On Mendeleev’s quadrature formula
Computational Mathematics and Mathematical Physics, 2012Summary: It is well known that D. I. Mendeleev was also an outstanding numerical mathematician, but few people know that he devised and frequently applied a quadrature formula, which can be named after him.
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Latin rectangles and quadrature formulas
European Journal of Combinatorics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nikolai M. Dobrovol'skii +3 more
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Mathematical Proceedings of the Cambridge Philosophical Society, 1950
1. It is frequently required to find the numerical value of the definite integralIt is, however, often found that even if the analytical expression off(x) is given, it cannot be integrated in terms of known elementary functions. The elliptic integrals are perhaps the best known examples of functions of this type; and more common are cases wheref(x) is ...
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1. It is frequently required to find the numerical value of the definite integralIt is, however, often found that even if the analytical expression off(x) is given, it cannot be integrated in terms of known elementary functions. The elliptic integrals are perhaps the best known examples of functions of this type; and more common are cases wheref(x) is ...
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RATIONAL FUNCTIONS AND QUADRATURE FORMULAE
Analysis, 1988Summary: In the theory of classical, strong and trigonometric moment problems quadrature formulae for the linear functional, defined by the moments, can be obtained by using ordinary or modified approximants of certain continued fractions as intermediaries.
Njåstad, Olav, Thron, W. J.
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