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  • 1970-1974  (1)
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    Electronic Resource
    Electronic Resource
    On the number of nodes in self-contained integration formulas of degree two for compact planar regions (1970)
    Springer
    Numerische Mathematik 16 (1970), S. 224-230 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Approximate integration formulas of precision two for compact planar regions are studied. We restrict our attention to formulas for which the nodes lie in the region and consider the problem of determining the minimum number of nodes attainable. While Stroud has shown that this minimum number is always at least 3, we find a two-parameter family of symmetric star-shaped regions for which it is equal to 4. That is, the conditions of symmetry and star-shapedness are not sufficient for the existence of such formulas with the minimal number of nodes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02219774
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