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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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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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Доклады Академии наук, 2018
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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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BIT, 1973
The problem of finding optimal quadrature formulas of given precision which minimize the sum of the absolute values of the quadrature weights is discussed and some optimal predictor and corrector type quadrature formulas are listed. Alternative derivation of minimum variance and Sard's optimal quadrature formulas is also given.
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The problem of finding optimal quadrature formulas of given precision which minimize the sum of the absolute values of the quadrature weights is discussed and some optimal predictor and corrector type quadrature formulas are listed. Alternative derivation of minimum variance and Sard's optimal quadrature formulas is also given.
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Russian Mathematical Surveys, 2005
In this survey we consider results and open problems related to two major ideas in the theory of optimal quadrature formulae: the ideas of Gauss and Kolmogorov.
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In this survey we consider results and open problems related to two major ideas in the theory of optimal quadrature formulae: the ideas of Gauss and Kolmogorov.
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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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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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New symmetric interpolatory quadrature formulas
Calcolo, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
FAVATI P, LOTTI G, ROMANI, FRANCESCO
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