The remainder term for analytic functions of Gauss-Lobatto quadratures

Schira, Thomas

doi:10.1016/s0377-0427(96)00100-8

Cited by 18 publications

(12 citation statements)

References 10 publications

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“…For the kernel K Lo m+2 (z; w 1/2 ) Schira [9] proved that for n ≥ 3 max This confirms some empirical results about the behavior of |K Lo n+2 (z; w 1/2 )| obtained in [1].…”

Section: Proof Of Resultssupporting

confidence: 82%

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On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions

Hunter

Nikolov

1999

Math. Comp.

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Abstract. Gauss-Lobatto quadrature formulae associated with symmetric weight functions are considered. The kernel of the remainder term for classes of analytic functions is investigated on elliptical contours. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with either the real or the imaginary axis. The results obtained here are an analogue of some recent results of T. Schira concerning Gaussian quadratures.

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“…For the kernel K Lo m+2 (z; w 1/2 ) Schira [9] proved that for n ≥ 3 max This confirms some empirical results about the behavior of |K Lo n+2 (z; w 1/2 )| obtained in [1].…”

Section: Proof Of Resultssupporting

confidence: 82%

“…For the kernel of the Gauss-Lobatto quadrature formula with double end nodes with respect to the first Chebyshev weight, Gautschi and Li [3] have proved that as solutions of certain equations, as was done in [9]. Alternatively, an upper bound for (m) can be obtained by a direct application of Lemmas 2.3 and 2.4 to |µ m+1 (z)|.…”

Section: Proof Of Resultsmentioning

confidence: 96%

On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions

Hunter

Nikolov

1999

Math. Comp.

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“…Some of the results have been extended to Gauss-Radau and Gauss-Lobatto formulas (cf. Gautschi [6], Gautschi and Li [7], Schira [37], Hunter and Nikolov [18]). …”

Section: The Remainder Term In Gauss-turán Quadrature Formulaementioning

confidence: 99%

Error bounds for Gauss-Turán quadrature formulae of analytic functions

Milovanović

Spalević

2003

Math. Comp.

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“…They applied it to several kinds of interpolatory and non-interpolatory quadrature rules. Error bounds for Gaussian quadratures of analytic functions were studied by Gautschi and Varga [5] (see also [6]), and later by Schira [15,16], Hunter and Nikolov [8].…”

Section: 1])mentioning

confidence: 99%

Maximum of the modulus of kernels in Gauss-Turán quadratures

2007

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Abstract. We study the kernels K n,s (z) in the remainder terms R n,s (f ) of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at ±1, when the weight ω is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel |K n,s (z)| attains its maximum on the real axis (positive real semi-axis) for each n ≥ n 0 , n 0 = n 0 (ρ, s). It was stated as a conjecture in [Math. Comp. 72 (2003), 1855-1872. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turán quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each n ≥ n 0 , n 0 = n 0 (ρ, s). Numerical examples are included.

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The remainder term for analytic functions of Gauss-Lobatto quadratures

Cited by 18 publications

References 10 publications

On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions

On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions

Error bounds for Gauss-Turán quadrature formulae of analytic functions

Maximum of the modulus of kernels in Gauss-Turán quadratures

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