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Empirical Means on Pseudo-Orthogonal Groups

Author

Listed:
  • Jing Wang

    (School of Information, Beijing Wuzi University, Beijing 101149, China)

  • Huafei Sun

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Simone Fiori

    (Dipartimento di Ingegneria dell’Informazione, Università Politecnica delle Marche, 60026 Ancona, Italy)

Abstract

The present article studies the problem of computing empirical means on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm.

Suggested Citation

  • Jing Wang & Huafei Sun & Simone Fiori, 2019. "Empirical Means on Pseudo-Orthogonal Groups," Mathematics, MDPI, vol. 7(10), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:940-:d:275190
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    References listed on IDEAS

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