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.
RELIABLE SOLUTION OF BIDIAGONAL SYSTEMS WITH APPLICATIONS / I., BAR ON; Leoncini, Mauro. - In: BIT. - ISSN 0006-3835. - STAMPA. - 39:(1999), pp. 403-416.
RELIABLE SOLUTION OF BIDIAGONAL SYSTEMS WITH APPLICATIONS
LEONCINI, Mauro
1999
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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