Fehlerabsch�tzungen f�r nichtsymmetrische Gau�-Quadraturformeln

Akrivis, Georgios; Burgstaller, A.

doi:10.1007/bf01389455

Cited by 7 publications

(6 citation statements)

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“…In [1] and [2], estimates for ||ÄJ| were derived for weight functions satisfying (1.6) or (1.7), and ||ÄJ| was given for w = W. Starting from (1.10) or (1.13) respectively, in the next section we calculate the norm of Rn for weight functions w with w=W/p" i = 1,2,…”

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The error norm of certain Gaussian quadrature formulae

Akrivis¹

1985

Math. Comp.

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We consider Gauss quadrature formulae Qn, ne N, approximating the integral 1(f)--/_\ w(x)f(x)dx, w = W/p,,i = 1,2, with W(x) = (1 -x)a(l + x)ß,a,ß = +1/2 and Pi(jc) = 1 + a2 + 2ax, p2(x) = (2b + l)x2 + b2, b > 0. In certain spaces of analytic functions the error functional R" '.-I -Q" is continuous. In [1] and [2] estimates for ||Ä"|| are given for a wide class of weight functions. Here, for a restricted class of weight functions, we calculate the norm of Rn explicitly. K = 0

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The error norm of certain Gaussian quadrature formulae

Akrivis¹

1985

Math. Comp.

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“…The II R. I[ has been computed explicitly in [1,2] for the Chebyshev weight functions of any of the four kinds, and in [3] 0<~<B, 3+2~, lal</~-~.…”

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The error norm of Gaussian quadrature formulae for weight functions of Bernstein-Szeg� type

Notaris

1990

Numer. Math.

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Summary.We consider the Gaussian quadrature formulae for the BernsteinSzeg6 weight functions consisting of any one of the four Chebyshev weights divided by an arbitrary quadratic polynomial that remains positive on [-i, 1]. Using the method in Akrivis (1985), we compute the norm of the error functional of these quadrature formulae. The quality of the bounds for the error functional, that can be obtained in this way, is demonstrated by two numerical examples.

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“…where is a seminorm in X r . It can be shown that R n is a continuous linear functional in (X r , | • | r ), and its norm is given by (see [2,4,26])…”

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