Department of Mathematics and Statistics
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This collection contains pre-prints and post-prints of journal articles written by selected York University Mathematics faculty.
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Browsing Department of Mathematics and Statistics by Author "Abrarov, S. M."
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Item Open Access Efficient algorithmic implementation of the Voigt/complex error function based on exponential series approximation(Elsevier, Applied Mathematics and Computation, 2011-11-01) Abrarov, S. M.; Quine, B. M.We show that a Fourier expansion of the exponential multiplier yields an exponential series that can compute high-accuracy values of the complex error function in a rapid algorithm. Numerical error analysis and computational test reveal that with essentially higher accuracy it is as fast as FFT-based Weideman’s algorithm at a regular size of the input array and considerably faster at an extended size of the input array. As this exponential series approximation is based only on elementary functions, the algorithm can be implemented utilizing freely available functions from the standard libraries of most programming languages. Due to its simplicity, rapidness, high-accuracy and coverage of the entire complex plane, the algorithm is efficient and practically convenient in numerical methods related to the spectral line broadening and other applications requiring error-function evaluation over extended input arrays.Item Open Access Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function(Journal of Mathematics Research, 2014-06) Abrarov, S. M.; Quine, B. M.We obtain a rational approximation of the Voigt/complex error function by Fourier expansion of the exponential function ${e^{ - {{\left( {t - 2\sigma } \right)}^2}}}$ and present master-slave algorithm for its efficient computation. The error analysis shows that at $y > {10^{ - 5}}$ the computed values match with highly accurate references up to the last decimal digits. The common problem that occurs at $y \to 0$ is effectively resolved by main and supplementary approximations running computation flow in a master-slave mode. Since the proposed approximation is rational function, it can be implemented in a rapid algorithm.Item Open Access On the Fourier expansion method for highly accurate computation of the Voigt/complex error function in a rapid algorithm(2012-06-21) Abrarov, S. M.; Quine, B. M.In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified representation of the proposed complex error function approximation makes possible further algorithmic optimization resulting in a considerable computational acceleration without compromise on accuracy.Item Open Access The rational number u2 for the two-term Machin-like formula for pi computed by iteration(2017-06-02) Abrarov, S. M.; Quine, B. M.