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Stability of Levinson algorithm for Toeplitz-like Systems

Numerical stability of the Levinson algorithm generalized for Toeplitz-like systems, is studied. Arguments based on the analytic results of an error analysis for floating point arithmetic produce an exponential upper bound on the norm of the residual vector. The base of such exponential function can be small for a class of
matrices containing point row diagonally dominant matrices.
Numerical experiments  show that, for this class, Gaussian elimination by row and Levinson algorithm have residuals of the same order of magnitude. As expected, the empirical results point out that the theoretical bound is too pessimistic.


Autori esterni: Grazia Lotti (Università di Pisa), Ornella Menchi (Università di Pisa)
Autori IIT:

Tipo: TR Rapporti tecnici
Area di disciplina: Mathematics
IIT TR 2/2009
Technical Report IIT TR-02/2009
File: 2009-TR-002.pdf

Attività: Metodi numerici per problemi di grandi dimensioni