How Fast can Moore’s Interval Integration Method Really be?
Moore’s interval integration method which uses only function evaluations of the integrant is interpreted as an approximation of the fundamental integration by Riemann-sums. In this way we can estimate the speed of convergence of this method and it is shown that its convergence factor of its linear convergence rate is bounded to below. This lower bound is shown to be sharp in the sense that there is a wide dass of functions for which it cannot be improved. In particular this is true for all rational functions only considered by Moore.
KeywordsRational Expression Interval Arithmetic Outer Approximation Integration Error Interval Extension
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