Abstract
In this work numerical methods for integration with respect to binomial measures are considered. Binomial measures are examples of fractal measures and arise when multifractal properties are investigated. Interpolatory quadrature rules are considered. An automatic integrator with local quadrature rules that generalize the five points Newton Cotes formula and error estimates based on null rules is then described. Numerical tests are performed to verify the efficiency and accuracy of the method. These tests confirm that the automatic integrator turns out to be as good as one of the best known quadrature algorithms with respect to the Lebesgue measure.
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AMS subject classification (2000)
28A25, 60G18, 65D30, 65D32, 68M15
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Calabrò, F., Corbo Esposito, A. An efficient and reliable quadrature algorithm for integration with respect to binomial measures . Bit Numer Math 48, 473–491 (2008). https://doi.org/10.1007/s10543-008-0168-x
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DOI: https://doi.org/10.1007/s10543-008-0168-x