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  • CR: 5.16
  • Springer  (4)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
  • Wiley
  • 2005-2009
  • 1990-1994
  • 1980-1984  (4)
  • 2008
  • 2006
  • 1982  (4)
Collection
Keywords
Publisher
  • Springer  (4)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
    • +
Years
  • 2005-2009
  • 1990-1994
  • 1980-1984  (4)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Quadrature formulas for oscillatory integral transforms (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 351-360 
    Details
    ISSN: 0945-3245
    Keywords: AMS: 65D30, 65R10 ; CR: 5.16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Quadrature formulas are obtained for the Fourier and Bessel transforms which correspond to the well-known Gauss-Laguerre formula for the Laplace transform. These formulas provide effective asymptotic approximations, complete with error bounds. Comparison is also made between the quadrature formulas and the asymptotic expansions of these transforms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407868
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  • 2
    Electronic Resource
    Electronic Resource
    Monotony in interpolatory quadratures (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 421-428 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D30 ; CR: 5.16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Let $$f(z) = \sum\limits_{j = 0}^\infty {t_{2j} z^{2j} } ,t_{2j} \geqq 0(j = 0,1,2,...)$$ , be holomorphic in an open disc with the centrez 0=0 and radiusr〉1. LetQ n (n=1, 2, ...) be interpolatory quadrature formulas approximating the integral $$\int\limits_{ - 1}^{ + 1} {f(x)dx} $$ . In this paper some classes of interpolatory quadratures are considered, which are based on the zeros of orthogonal polynomials corresponding to an even weight function. It is shown that the sequencesQ n 9f] (n=1, 2, ...) are monotone. Especially we will prove monotony in Filippi's quadrature rule and with an additional assumption onf monotony in the Clenshaw-Curtis quadrature rule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407873
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal quadrature formula of Markov's and Locher's type with weight function (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 31-37 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65D30 ; CR: 5.16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A quadrature formula of Markov's type with a weight functionx α(1−x)β, which has properties of formulas exact for polynomials of a given degree and properties of optimal formulas on some sets of functions, is given. The particular case of formula (where α=β=p=q=0) is the formula of Locher [1, 2].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459072
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  • 4
    Electronic Resource
    Electronic Resource
    Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 347-363 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D30 ; CR: 5.16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The IMT rule, which is especially suited for the integration of functions with end-point singularities, is generalized by introducing parameters and also by repeatedly applying the parametrized IMT transformation. The quadrature formulas thus obtained are improved considerably both in efficiency and in robustness against end-point singularities. Asymptotic error estimates and numerical results are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396437
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