Summary
Subject to rather mild assumptions on the integrand, the Romberg table (theT-table) and the modified Romberg table (theU-table) yield asymptotically upper and lower bounds for the value of the integral, and the convergence of the columns of the two tables is asymptotically monotone. This is verified for arbitrary sequences of step sizes satisfying the usual condition of convergence for Romberg integration.
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Literatur
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