Results 11 to 20 of about 217,218 (245)
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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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.
Trefethen, Lloyd N
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On Birkhoff Quadrature Formulas [PDF]
Proceedings of the American Mathematical Society, 1986 In an earlier work the author has obtained new quadrature formulas (see (1.3)) based on function values and second derivatives on the zeros of
A. K. Varma
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Error estimation for quadrature formulas based on equally spaced nodes [PDF]
Mathematical Modelling and Analysis, 2006 The error estimation for quadrature formulas based on equally spaced nodes is discussed in this paper. The error estimates use embedded formulas and they are obtained for Newton‐Cotes and Hermitian quadrature formulas.
K. Plukas, D. Plukiene
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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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Weighted Optimal Quadrature Formulas in Sobolev Space and Their Applications
AlgorithmsThe optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas.
Kholmat Shadimetov, Khojiakbar Usmanov
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Quadrature formulas for Fourier coefficients [PDF]
Journal of Computational and Applied Mathematics, 2009 \textit{C. A. Micchelli} and \textit{T. J. Rivlin} [IBM J. Res. Develop. 16, 372--379 (1972; Zbl 0288.65013)] discovered the remarkable fact that the quadrature \[ \int^1_{-1}T_n(t)f(t)\frac{dt}{\sqrt{1-t^2}}\approx \frac{\pi}{n2^n}f'[\xi_1, \dots,\xi_n] \] is exact for all algebraic polynomials of degree \(\leq 3n-1\), where \[ T_n(t):=\cos(n\text{arc}
Bojanov, Borislav, Petrova, Guergana
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Numerical quadrature methods for singular and nearly singular integrals [PDF]
, 2001 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis is concerned with the development, design, and analysis of simple and efficient numerical quadrature methods for integrals on finite intervals ...
Chunrungsikul, Sumlearng
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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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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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