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Reliable Solution of Bidiagonal Systems with Applications

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Abstract

We show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems.

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Authors and Affiliations

  1. Department of Chemistry, Technion, Haifa, 32000, Israel, email: baron@cs.technion.ac.il

    Ilan Bar-On

  2. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, IT-56125, Pisa, Italy. email: leoncini@imc.pi.cnr.it

    Mauro Leoncini

Authors
  1. Ilan Bar-On
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  2. Mauro Leoncini
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Bar-On, I., Leoncini, M. Reliable Solution of Bidiagonal Systems with Applications. BIT Numerical Mathematics 39, 403–416 (1999). https://doi.org/10.1023/A:1022310417356

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  • DOI: https://doi.org/10.1023/A:1022310417356

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