Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space \(L_{2}^{(m)}(0,1)\)

DOI10.1007/s11075-016-0150-7zbMath1364.65302OpenAlexW2481651326MaRDI QIDQ509631

N. D. Boltaev, Abdullo Rakhmonovich Hayotov, Kholmat Mahkambaevich Shadimetov

Publication date: 17 February 2017

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-016-0150-7

zbMATH Keywords

numerical exampleSobolev spaceconvolutionHilbert spaceFourier coefficientshighly oscillatory functionsextremal functionFourier integralerror functionalexact quadrature formulaoptimal coefficientsoptimal quadrature formulasSard's problem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (9)

Optimal formulas for the approximate-analytical solution of the general Abel integral equation in the Sobolev space ⋮ Optimal quadrature formulas for oscillatory integrals in the Sobolev space ⋮ Optimal quadrature formulas for calculating integrals of rapidly oscillating functions ⋮ OPTIMAL QUADRATURE FORMULAS FOR FOURIER COEFFICIENTS IN <i>W</i>₂^{(<i>m</i>,<i>m</i>-1)} 2 SPACE ⋮ Application of optimal quadrature formulas for reconstruction of CT images ⋮ Optimal quadrature formulas for the Sobolev space \(H^1\) ⋮ Construction of optimal quadrature formulas exact for exponentional-trigonometric functions by Sobolev's method ⋮ Оптимальные формулы типа Эйлера-Маклорена для численного интегрирования в пространстве Соболева ⋮ On an optimal quadrature formula for approximation of Fourier integrals in the space \(L_2^{( 1 )}\)

Cites Work

• Complexity of oscillatory integration for univariate Sobolev spaces
• Optimal quadrature formulas with positive coefficients in \(L_2^{(m)}(0, 1)\) space
• On an optimal quadrature formula in the sense of Sard
• Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures
• On the weights of Sard's quadrature formulas
• On optimal quadrature formulae
• Efficient computation of highly oscillatory integrals with Hankel kernel
• Optimal quadrature formula in \(K_2(P_2)\) space
• Optimal quadrature formulas in the sense of Sard in \(W_2^{(m,m-1)}\) space
• Numerical approximation of vector-valued highly oscillatory integrals
• Quadrature formulae
• Numerical Integration of Highly Oscillating Functions
• On Semicardinal Quadrature Formulae
• Efficient quadrature of highly oscillatory integrals using derivatives
• Optimal quadrature formulae
• On Monosplines of Least Deviation and Best Quadrature Formulae
• On Monosplines of Least Square Deviation and Best Quadrature Formulae II
• Best Approximate Integration Formulas; Best Approximation Formulas
• Best Approximate Integration Formulas
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