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Minimum-volume ellipsoidal approximation of the sum of two ellipsoids

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Abstract

The problem of the ellipsoidal approximation of the sum of two ellipsoids optimal with respect to the minimum of multidimensional volume is considered. It is solved without the use of affinities and representation as a conditional optimization problem. The case of simultaneous degeneracy of the ellipsoids is considered. A geometrical interpretation of the approximation is given. Results of the numerical modeling are presented.

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Authors and Affiliations

  1. Institute of Applied Systems Analysis, National Technical University of Ukraine “Kyiv Polytechnic Institute,” National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kyiv, Ukraine

    O. V. Sholokhov

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  1. O. V. Sholokhov
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Correspondence to O. V. Sholokhov.

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 138–144, November–December 2011.

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Sholokhov, O.V. Minimum-volume ellipsoidal approximation of the sum of two ellipsoids. Cybern Syst Anal 47, 954–960 (2011). https://doi.org/10.1007/s10559-011-9375-6

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  • DOI: https://doi.org/10.1007/s10559-011-9375-6

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