Results 191 to 200 of about 1,730 (224)

An optimal quadrature formula in the Sobolev space

Uzbek Mathematical Journal, 2021
This 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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On optimal quadrature formulas

Journal of Applied and Industrial Mathematics, 2007
Quadrature 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

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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Optimal weighted chebyshev-type quadrature formulas

Calcolo, 1975
A 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 formulae

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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The Coefficients of Optimal Quadrature Formulas

2006
2 (R) are studied by means of a variational method. Here w(x) is a weight function, χΩ(x) is the characteristic function of the interval Ω, and c(β) are the coefficients of the quadrature formula. The results generalize some results by A. Sard, L. F. Meyers, I. J. Schoenberg, S. D. Silliman (1-4), and others derived by the method of splines.
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Optimal quadrature formulas for a sphere

USSR Computational Mathematics and Mathematical Physics, 1977
Abstract The problem of finding the statistically optimal quadrature formula for a sphere is posed. A system of linear algebraic equations satisfied by weights of the quadrature formula is written down. Two examples are given. Asymptotic estimates of the relative error are 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).
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Optimal quadrature formulae for differentiable functions

Calcolo, 1986
The existence of an optimal quadrature formula of the form \(\int^{b}_{a}f| x| dx\approx \sum^{n}_{k=1}\sum^{\nu_ k-1}_{\lambda =0}a_{k\lambda}f^{(\lambda)}(xk)\) with preassigned multiplicities \((\nu_ k)_ 1^ n\) in the classes \(LW_ q^ r:=\{f\in C^{(r-1)}:f^{(r-1)}\)- abs.
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A WEIGHTED OPTIMAL QUADRATURE FORMULA WITH DERIVATIVE

UZBEK MATHEMATICAL JOURNAL
This article focuses on the derivation and analysis of a weighted optimal quadra- ture formula in the Hilbert space W (2,1) 2 (0, 1). The formula is expressed as a linear combination of function values and its first-order derivatives at equidistant nodes in the interval [0, 1].
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