Gauss-Radau and Gauss-Lobatto interval quadrature rules for Jacobi weight function

Milovanović, Gradimir V.; Cvetković, Aleksandar S.

doi:10.1007/s00211-005-0650-1

Cited by 5 publications

(2 citation statements)

References 6 publications

(9 reference statements)

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“…Interval quadrature formulae have been considered by many mathematicians (see for instance [18,20,13,21,4,17,15]). The results about optimal interval quadrature formula for the classes of differentiable periodic functions are known for the classes W r 1 [4], W r ∞ [17], and W 1 F [7,8].…”

Section: Background Main Results Scheme Of the Proofmentioning

confidence: 99%

On the best interval quadrature formulae for classes of differentiable periodic functions

Бабенко

Skorokhodov

2007

Journal of Complexity

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In this paper we solve the problem about optimal interval quadrature formula for the class W r F of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearrangements of averaged monosplines is proved.

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Section: Background Main Results Scheme Of the Proofmentioning

confidence: 99%

On the best interval quadrature formulae for classes of differentiable periodic functions

Бабенко

Skorokhodov

2007

Journal of Complexity

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“…For the special case of the Chebyshev weight of the first kind and the special set of lengths an analytic solution can be given [29]. Interval quadrature rules of Gauss-Radau and Gauss-Lobatto type with respect to the Jacobi weight functions are considered in [33].…”

Section: Introductionmentioning

confidence: 99%

Nonstandard Gaussian quadrature formulae based on operator values

Milovanović

Cvetković

2009

Adv Comput Math

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In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear operators we obtain interesting explicit results connected with theory of orthogonal polynomials.Keywords Gaussian quadrature · Interval quadrature · Linear operator · Zeros · Weight · Measure · Degree of exactness · Orthogonal polynomial · Linear functional Mathematics Subject Classifications (2000) 41A55 · 33C45 · 33D45 · 65D30 · 65D32

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The Scientific Work of Gradimir V. Milovanović

Ivić

2010

Approximation and Computation

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Gauss-Radau and Gauss-Lobatto interval quadrature rules for Jacobi weight function

Cited by 5 publications

References 6 publications

On the best interval quadrature formulae for classes of differentiable periodic functions

On the best interval quadrature formulae for classes of differentiable periodic functions

Nonstandard Gaussian quadrature formulae based on operator values

The Scientific Work of Gradimir V. Milovanović

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