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  • 1
    Electronic Resource
    Electronic Resource
    Some results about numerical quadrature on the unit circle (1996)
    Springer
    Advances in computational mathematics 5 (1996), S. 297-328 
    Details
    ISSN: 1572-9044
    Keywords: Distribution functions ; integration rules ; interpolation nodes ; Szegö polynomials ; 41 ; 65D
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, quadrature formulas on the unit circle are considered. Algebraic properties are given and results concerning error and convergence established. Finally, numerical experiments are carried out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02124749
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence of Gaussian Quadrature and Lagrange Interpolation in Haar Systems (1999)
    Springer
    BIT 39 (1999), S. 579-584 
    Details
    ISSN: 1572-9125
    Keywords: Markov system ; Gaussian formulas ; Lagrange interpolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consider a Markov system of functions whose linear span is dense with respect to the uniform norm in the space of the continuous functions on a finite interval. Gaussian rules are those which correctly integrate as many successive basis functions as possible with the lesser number of nodes. In this paper we provide a simple proof of the fact that such rules converge for all bounded Riemann-Stieltjes integrable functions. The proposed proof is also valid for any sequence of quadrature rules with positive coefficients which converge for the basis functions. Taking the nodes of the Gaussian rules as nodes for Lagrange interpolation, we give a sufficient condition for the convergence in L 2-norm of such processes for bounded Riemann-Stieltjes integrable functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022378905061
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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