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.
BIT
39
403
416
RELIABLE SOLUTION OF BIDIAGONAL SYSTEMS WITH APPLICATIONS / I., BAR ON; Leoncini, Mauro. - In: BIT. - ISSN 0006-3835. - STAMPA. - 39:(1999), pp. 403-416.
I., BAR ON; Leoncini, Mauro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/454039
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