Abstract
We describe how weight functions are implemented in SVALAQ, Self-Validating Adaptive Quadrature, to provide a self-validating computation of the definite integral equation
SVALAQ computes an interval [c,d] in which If is guaranteed to lie. The inclusion is validated by SVALAQ, provided that f(x) can be evaluated on all of [A,B] or if f(x) has certain singularities.
Rules for evaluating definite integrals using weight functions in a self-validating environment were also developed. These rules, based on Taylor’s polynomials, cover some of the difficulties associated with certain algebraic, logarithmic and sinusoidal weight functions in validated quadrature.
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References
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© 1987 D. Reidel Publishing Company
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Krenz, G.S. (1987). Using Weight Functions in Self-Validating Quadrature. 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_26
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DOI: https://doi.org/10.1007/978-94-009-3889-2_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8227-3
Online ISBN: 978-94-009-3889-2
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