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Focal approximation on the complex plane

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Abstract

The problem of analytic approximation of a smooth closed curve specified by a set of its points on the complex plane is proposed. An algorithmic method for constructing an approximating lemniscate is proposed and investigated. This method is based on a mapping of the curve to be approximated onto the phase circle; the convergence of the method is proved. The location of the lemniscate foci inside the curve provides the degrees of freedom for the focal approximation.

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Authors and Affiliations

  1. Institute of Engineering Science, Russian Academy of Sciences, Malyi Khariton’evskii per. 4, Moscow, 101990, Russia

    T. A. Rakcheeva

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  1. T. A. Rakcheeva
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Correspondence to T. A. Rakcheeva.

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Original Russian Text © T.A. Rakcheeva, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 11, pp. 1963–1972.

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Rakcheeva, T.A. Focal approximation on the complex plane. Comput. Math. and Math. Phys. 51, 1847–1855 (2011). https://doi.org/10.1134/S0965542511110145

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  • DOI: https://doi.org/10.1134/S0965542511110145

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