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Gröbner basis computation of Drazin inverses with multivariate rational function entries

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  • Sendra, Juana
  • Rafael Sendra, J.

Abstract

In this paper we show how to apply Gröbner bases to compute the Drazin inverse of a matrix with multivariate rational functions as entries. When the coefficients of the rational functions depend on parameters, we give sufficient conditions for the Drazin inverse to specialize properly. In addition, we extend the method to weighted Drazin inverses. We present an empirical analysis that shows a good timing performance of the method.

Suggested Citation

  • Sendra, Juana & Rafael Sendra, J., 2015. "Gröbner basis computation of Drazin inverses with multivariate rational function entries," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 450-459.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:450-459
    DOI: 10.1016/j.amc.2015.02.070
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    Cited by:

    1. Stanimirović, Predrag S. & Ćirić, Miroslav & Lastra, Alberto & Sendra, Juan Rafael & Sendra, Juana, 2021. "Representations and symbolic computation of generalized inverses over fields," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    2. Sendra, J. Rafael & Sendra, Juana, 2017. "Computation of Moore–Penrose generalized inverses of matrices with meromorphic function entries," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 355-366.
    3. Chan, Eunice Y.S. & Corless, Robert M. & González-Vega, Laureano & Sendra, J. Rafael & Sendra, Juana, 2022. "Inner Bohemian inverses," Applied Mathematics and Computation, Elsevier, vol. 421(C).

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