Geodesic
Preconditioning block Toeplitz matrices
Electronic transactions on numerical analysis, Tome 29 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We investigate the spectral behavior of preconditioned block Toeplitz matrices with small non- Toeplitz blocks. These matrices have a quite different behavior than scalar or mulitlevel Toeplitz matrices. Based on the connection between Toeplitz and Hankel matrices we derive some negative results on eigenvalue clustering for ill-conditioned block Toeplitz matrices. Furthermore, we identify Block Toeplitz matrices that are easy to solve by the preconditioned conjugate gradient method. We derive some useful inequalities that give information on the location of the spectrum of the preconditioned systems. The described analysis also gives information on preconditioning ill-conditioned Toeplitz Schur complement matrices and Toeplitz normal equations.
Classification : 65F10, 65F15
Keywords: Toeplitz, block Toeplitz, Schur complement, preconditioning, conjugate gradient method 
@article{ETNA_2008__29__a11,
     author = {Huckle, Thomas K. and Noutsos, Dimitrios},
     title = {Preconditioning block {Toeplitz} matrices},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a11/}
}
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Huckle, Thomas K.; Noutsos, Dimitrios. Preconditioning block Toeplitz matrices. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a11/