Results 61 to 70 of about 2,749,932 (104)
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BIT Numerical Mathematics, 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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On optimization of weight quadrature formulas
Ukrainian Mathematical Journal, 1995 We obtain asymptotically optimal quadrature formulas on the classH ω [-1, 1] for an arbitrary continuous weight function which is positive on [-1, 1] almost everywhere and for a wide class of moduli of continuity ω(t).
Бабенко, В.Ф.
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Error Inequalities for an Optimal Quadrature Formula
Journal of Applied Mathematics and Computing, 2007An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.
Nenad Ujević
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On an optimal quadrature formula in the sense of Sard
Numerical Algorithms, 2010Let \(K_2 = \{\varphi:\,[0,1] \to \mathbb R\); \(\varphi'\) absolutely continuous and \(\varphi'' \in L_2(0,1)\}\) be the Hilbert space with the semi-norm \[ \|\varphi\| = \bigg(\int_0^1 (\varphi''(x) + 1)^2\,dx\bigg)^{1/2}. \] Then the quadrature formula \[ \int_0^1 \varphi(x)\, dx \approx \sum_{\nu =0}^N C_{\nu}\,\varphi(x_{\nu}) \] has the error ...
Abdullo Rakhmonovich Hayotov +2 more
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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.
A. H. Wang, R. L. Klein
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Application of optimal quadrature formulas for reconstruction of CT images
Journal of Computational and Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdullo Rakhmonovich Hayotov +2 more
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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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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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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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An optimal quadrature formula in the Sobolev space
Uzbek Mathematical Journal, 2021This paper studies the problem of construction of optimal quadrature formulas for approximate calculation of integrals with trigonometric weight in the L(2m)(0, 1) space for any ω = 0, ω ∈ R. Here explicit formulas for the optimal coefficients are obtained. We study the order of convergence of the optimal formulas for the case m = 1, 2.
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