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Mathematics of Computation

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On the nonexistence of simplex integration rules for infinite integrals


Authors: P. J. Davis and P. Rabinowitz
Journal: Math. Comp. 26 (1972), 687-688
MSC: Primary 65D30
MathSciNet review: 0326999
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Abstract: It is shown that there do not exist integration rules of the form

$\displaystyle \int_0^\infty {f(x)} dx = \sum\limits_{i = 1}^n {{w_{_i}}f({x_i}) + {C_n}{f^{(m)}}(\xi ),\quad 0 < \xi < \infty .} $


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0326999-0
Keywords: Numerical integration, infinite interval, simplex rule, integration error
Article copyright: © Copyright 1972 American Mathematical Society