Results 71 to 80 of about 2,749,932 (104)

An Approach to the Investigation of Optimal Quadrature Formulas for Singular Integrals With Fixed Singularity

Ukrainian Mathematical Journal, 1995
Для класів функцій, заданих на відрізку [0,1], знайдені оптимальні квадратурні формули для сингулярних інтегралів з фіксованою особливістю. Одержані результати поширюються для двовимірних інтегралів.For classes of functions given on the segment [0,1], we
Шабозов, М.Ш.
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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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Optimal quadrature formulas with derivatives in a periodic space

AIP Conference Proceedings, 2021
The paper is devoted to investigation of optimal formulas for approximate integration with derivatives in the Sobolev space L2(m)˜(0,1) of periodic functions. Here the extremal function for quadrature formulas of Hermite type is obtained. Applying this extremal function the square of the norm for the error functional of the considered Hermite type ...
Kholmat Shadimetov, Nilufar Mamatova
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Asymptotic Properties of Optimal Quadrature Formulas

1979
In [9], Sard introduced a notion of “best” for quadrature formulas which may be described as follows. Let 0 = t0 < t1 < ... < tN = 1 be fixed points, and consider the formula $${Q_N}(f) \equiv \sum\limits_{i = 0}^N {{c_i}f({t_i}) \simeq \int_0^1 f (\tau )} d\tau \equiv I(f)$$ (1) .
David L. Barrow, Philip W. Smith
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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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An optimal quadrature formula in K2(P3) space

AIP Conference Proceedings, 2021
In this paper in K2(P3) Hilbert space the problem of construction of optimal quadrature formula in the sense of Sard is considered and using S.L. Sobolev’s method a new optimal quadrature formula is obtained. For the optimal coefficients explicit formulas are given.
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Optimal stochastic quadrature formulas for convex functions

BIT, 1994
Optimal stochastic (Monte Carlo) quadrature formulas for defined classes of convex functions are studied. Specifically, non-adaptive Monte Carlo methods are seen to be no better than deterministic methods, but adaptive Monte Carlo methods are shown to exhibit a superior performance.
Novak, E., Petras, K.
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A numerical method to obtain optimal quadrature formulas

International Journal for Numerical Methods in Engineering, 1978
AbstractThis paper present a numerical method to obtain optimal quadrature formulas of Gauss type and Radau type in the sense of Sard. Using the relation between optimal quadrature formulas and nonospline functions, the optimal quadrature formula can be obtained by solving a set of no‐linear simultaneous algebraic equations induced from the ...
Wang, A. H., Klein, R. L.
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