Results 1 to 10 of about 1,199 (217)
Convergence of Gaussian Quadrature Formulas
Journal of Approximation Theory, 2000 Classical Gaussian formulas are well known. They construct a polynomial interpolating in the zeros of a polynomial orthogonal with respect to a positive measure \(\alpha\) and the integral of this polynomial is a quadrature formula for \(\int f(x) d\alpha(x)\) with maximal polynomial degree of exactness.
Ying Guang Shi
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Some new kinds of interpolation formulas and its applications [PDF]
Mathematics and Computational Sciences, 2022 In this work, using the determination function, some new kinds of interpolation formulas are presented.These novel formulas are extensions of Lagrange interpolation. Error formula for these new kind of interpolation formulas are obtained.
M. A Jafari, A Aminataei
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Exactness of Quadrature Formulas [PDF]
SIAM Review, 2022 The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases: Newton-Cotes, Clenshaw-Curtis, Gauss-Legendre, and Gauss-Hermite quadrature.
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Axioms, 2022 The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels.
Ilya Boykov +2 more
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Optimal quadrature formulas for oscillatory integrals in the Sobolev space
Journal of Inequalities and Applications, 2022 This work studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space L 2 ( m ) ( 0 , 1 ) $L_{2}^{(m)}(0,1)$ for numerical calculation of Fourier coefficients. Using Sobolev’s method, we obtain new sine and cosine
Kholmat Shadimetov +2 more
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On semicardinal quadrature formulae [PDF]
Mathematics of Computation, 1974 The present paper concerns the semicardinal quadrature formulae introduced in Part III of the reference [3]. These were the limiting forms of Sard’s best quadrature formulae as the number of nodes increases indefinitely. Here we give a new derivation and characterization of these formulae.
Schoenberg, I. J., Silliman, S. D.
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Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula
Mathematics, 2022 As convexity plays an important role in many aspects of mathematical programming, e.g., for obtaining sufficient optimality conditions and in duality theorems, and one of the most important inequalities for convex functions is the Hermite–Hadamard ...
Josipa Barić
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Results in Applied Mathematics, 2022 This article discusses the development of a new algorithm, which is based on optimal quadrature formulas for obtaining solutions to the generalized Abel integral equations.
Kholmat M. Shadimetov +1 more
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Euler-Maclaurin type optimal formulas for numerical integration in Sobolev space
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2020 In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space L2(m)(0,1) is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third ...
Hayotov, A.R. +3 more
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On approximation of two-dimensional potential and singular operators [PDF]
E-Journal of Analysis and Applied Mathematics, 2019 The purpose of this paper is the construction of second-order of accuracy quadrature formulas for the numerical calculation of the Vekua types two-dimensional potential and singular integral operators in the unit disk of complex plane.
Charyyar Ashyralyyev, Sedanur Efe
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