An Error expansion for some Gauss-Turán quadratures and \(L^1\)-estimates of the remainder term

DOI10.1007/s10543-005-2643-yzbMath1082.41022OpenAlexW2335005764WikidataQ115058787 ScholiaQ115058787MaRDI QIDQ2568631

Miodrag M. Spalević, Gradimir V. Milovanović

Publication date: 18 October 2005

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-2643-y

zbMATH Keywords

zeroserror estimatemultiple nodesweightGauss-Turán quadratureerror expansioncontour integral representationremainder term for analytic functions

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items (16)

A note on the bounds of the error of Gauss--Turán-type quadratures ⋮ Gauss-Tur'an quadratures of Kronrod type for generalized Chebyshev weight functions ⋮ Error bounds of Micchelli-Rivlin quadrature formula for analytic functions ⋮ Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses -- survey of recent results ⋮ Error bounds for kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions ⋮ Kronrod extensions with multiple nodes of quadrature formulas for Fourier coefficients ⋮ Best quadrature formula on Sobolev class with Chebyshev weight ⋮ Bounds of the error of Gauss-Turán-type quadratures. II. ⋮ Monotonicity of the error term in Gauss-Turán quadratures for analytic function ⋮ The error norm of quadrature formulae ⋮ Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions ⋮ Maximum of the modulus of kernels in Gauss-Turán quadratures ⋮ The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type ⋮ The Scientific Work of Gradimir V. Milovanović ⋮ The Remainder Term of Gauss–Turán Quadratures for Analytic Functions ⋮ On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type

Cites Work

• Corrections to On the remainder term for analytic functions of Gauss- Lobatto and Gauss-Radau quadratures
• Error analysis in some Gauss-Turán-Radau and Gauss-Turán-Lobatto quadratures for analytic functions.
• Quadrature formulae connected to sigma-orthogonal polynomials
• Calculation of Gaussian-type quadratures with multiple nodes
• Some error expansions for Gaussian quadrature
• The remainder term for analytic functions of Gauss-Radau and Gauss- Lobatto quadrature rules with multiple end points
• Error Bounds for Gaussian Quadrature of Analytic Functions
• On the Remainder of Gaussian Quadrature Formulas for Bernstein-Szego Weight Functions
• Error bounds for Gauss-Turán quadrature formulae of analytic functions
• On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions
• A Note on the Contour Integral Representation of the Remainder Term for a Gauss–Chebyshev Quadrature Rule
• Error Estimates for Gauss Quadrature Formulas for Analytic Functions
• The remainder term for analytic functions of symmetric Gaussian quadratures
• The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function
• The remainder term for analytic functions of Gauss-Lobatto quadratures
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