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Medientyp:
E-Artikel
Titel:
Product Integration in the Presence of a Singularity
Beteiligte:
Rabinowitz, Philip;
Sloan, Ian H.
Erschienen:
Society for Industrial and Applied Mathematics, 1984
Erschienen in:SIAM Journal on Numerical Analysis
Sprache:
Englisch
ISSN:
0036-1429
Entstehung:
Anmerkungen:
Beschreibung:
<p>This paper considers the approximate evaluation of ∫<sup>b</sup><sub>a</sub> k(x)f(x) dx, where k is a fixed Lebesgue integrable function, by quadrature rules of the form ∑<sup>m<sub>n</sub></sup><sub>i=0</sub> w<sub>in</sub>f(x<sub>in</sub>). Normally rules of this kind are used only for smooth functions f, and any singularities are incorporated into k. Here, however, we allow f to have a singularity, either at an endpoint or in the interior. General convergence properties are established for a wide class of product integration rules. More detailed results are established for the class of rules which are exact if f belongs to a specified family of piecewise polynomials.</p>