Information-Based Complexity of Multivariate Integration in the Randomized and Quantum Model

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Abstract:

In this paper, we investigate the integration of the Hölder-Nikolskii classes MHr p 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.

Keywords: CONVERGENCE RATE; HÖLDER-NIKOLSKII CLASS; QUANTUM ALGORITHM; RANDOMIZED ALGORITHM

Document Type: Research Article

DOI: http://dx.doi.org/10.1166/asl.2012.2295

Publication date: March 1, 2012

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  • ADVANCED SCIENCE LETTERS is an international peer-reviewed journal with a very wide-ranging coverage, consolidates research activities in all areas of (1) Physical Sciences, (2) Biological Sciences, (3) Mathematical Sciences, (4) Engineering, (5) Computer and Information Sciences, and (6) Geosciences to publish original short communications, full research papers and timely brief (mini) reviews with authors photo and biography encompassing the basic and applied research and current developments in educational aspects of these scientific areas.
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