In the present paper we survey some results recently proposed by the author about the spectral properties of preconditioned Toeplitz matrices and we discuss the deep connections with the elegant theory introduced by G Szegö for nonpreconditioned Toeplitz matrices. Then, we briefly stress the potentiality of this new mathematical tool both with respect to the design of fast resolution methods for Toeplitz (and Toeplitz-related) systems and with respect to the problem of evaluating the asymptotic condition numbers of such operators
Sulle proprietà spettrali di matrici precondizionate di Toeplitz
SERRA CAPIZZANO, STEFANO
1997-01-01
Abstract
In the present paper we survey some results recently proposed by the author about the spectral properties of preconditioned Toeplitz matrices and we discuss the deep connections with the elegant theory introduced by G Szegö for nonpreconditioned Toeplitz matrices. Then, we briefly stress the potentiality of this new mathematical tool both with respect to the design of fast resolution methods for Toeplitz (and Toeplitz-related) systems and with respect to the problem of evaluating the asymptotic condition numbers of such operators
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