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  • 1
    Electronic Resource
    Electronic Resource
    On cubature formulae with a minimal number of knots (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 281-297 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D30 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper an approach is outlined to the two-dimensional analogon of the Gaussian quadrature problem. The main results are necessary and sufficient conditions for the existence of cubature formulae which are exact for all polynomials of degree ≦m and which have a minimal number of 1/2k(k+1) knots,k=[m/2]+1. Ifm is odd, similar results are due to I.P. Mysovskikh ([5, 6]) which will be derived in a new way as a special case of the general characterization given here. Furthermore, it will be shown how this characterization can be used to construct minimal formulae of even degree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397880
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