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Optimal weighted chebyshev-type quadrature formulas
Calcolo, 1975A weighted quadrature formula is called of Chebyshev type if it has equal coefficients and real (but not necessarily distinct) nodes. Among such quadrature rules we construct an optimal one, i. e., one which has maximum algebraic degree of accuracy and minimum error when applied to the first power not exactly integrated.
Anderson, L. A., Gautschi, Walter
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Optimal quadrature formula nonlinear estimators
Information Sciences, 1978Abstract This paper presents a method for the realization of nonlinear estimators based on an optimal quadrature approximation. The optimal quadrature formula is obtained by solving a set of nonlinear algebraic equations induced from a monospline subject to a set of interpolatory conditions.
Wang, A. H., Klein, R. L.
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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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Optimal quadrature formulas of Euler–Maclaurin type
Applied Mathematics and Computation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shadimetov, Kh. M. +2 more
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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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On optimal quadrature formulas
Journal of Applied and Industrial Mathematics, 2007Quadrature formulas with free nodes which are optimal in the norm of a Banach space are studied. It is shown that it is impossible with some reasonable assumptions to increase the accuracy of such a formula by defining the partial derivatives of the integrable function at the nodes.
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Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions
Journal of Mathematical Sciences, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shadimetov, Kholmat, Gulomov, Otabek
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