Abstract
It is shown that given a one-dimensional interpolatory integration rule with positive weights based on a set S of n points, it is possible to find a subset T of S containing n-1 points such that the weights of the interpolatory integration rule based on T are all nonnegative. Consequently, given any one-dimensional positive interpolatory integration rule R, we can generate a sequence of imbedded positive interpolatory rules starting with R. This idea of starting with a rule R and generating a sequence of imbedded rules, which is due to Patterson, can be applied to generate sequences of imbedded multidimensional integration rules. In this case, we do not aim for positive rules but for efficient rules. Some examples are given as to what can be attained.
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© 1987 D. Reidel Publishing Company
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Rabinowitz, P., Kautsky, J., Elhay, S., Butcher, J.C. (1987). On Sequences of Imbedded Integration Rules. In: Keast, P., Fairweather, G. (eds) Numerical Integration. NATO ASI Series, vol 203. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3889-2_13
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DOI: https://doi.org/10.1007/978-94-009-3889-2_13
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