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Differentiating matrix orthogonal transformations

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Abstract

New numerical algorithms for differentiating matrix orthogonal transformations are constructed. They do not require that the derivatives of the orthogonal transformation matrix be available. An example is given how these algorithms can be applied to the numerically stable calculation of a solution to the discrete-time matrix Riccati sensitivity equation.

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Authors and Affiliations

  1. CEMAT, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    M. V. Kulikova

  2. Ul’yanovsk State University, ul. L’va Tolstogo 42, Ul’yanovsk, 432600, Russia

    Yu. V. Tsyganova

Authors
  1. M. V. Kulikova
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  2. Yu. V. Tsyganova
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Correspondence to M. V. Kulikova.

Additional information

Original Russian Text © M.V. Kulikova, Yu.V. Tsyganova, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 9, pp. 1460–1473.

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Kulikova, M.V., Tsyganova, Y.V. Differentiating matrix orthogonal transformations. Comput. Math. and Math. Phys. 55, 1419–1431 (2015). https://doi.org/10.1134/S0965542515090109

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  • DOI: https://doi.org/10.1134/S0965542515090109

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