In this paper, we investigate the integration of the Hölder-Nikolskii classes MHrp pin the randomized and quantum computation model. We develop randomized and quantum algorithms for integration of functions from this class and analyze their convergence
rates. Comparing our results with the convergence rates in the deterministic set- ting, we see that quantum computing can reach an exponential speedup over deterministic classical computation and a quadratic speedup over randomized classical computation.
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