Abstract.
In earlier papers Tyrtyshnikov [42] and the first author [14] considered the analysis of clustering properties of the spectra of specific Toeplitz preconditioned matrices obtained by means of the best known matrix algebras. Here we generalize this technique to a generic Banach algebra of matrices by devising general preconditioners related to “convergent” approximation processes [36]. Finally, as case study, we focus our attention on the Tau preconditioning by showing how and why the best matrix algebra preconditioners for symmetric Toeplitz systems can be constructed in this class.
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Received April 25, 1997 / Revised version received March 13, 1998
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Di Benedetto, F., Serra Capizzano, S. A unifying approach to abstract matrix algebra preconditioning. Numer. Math. 82, 57–90 (1999). https://doi.org/10.1007/s002110050411
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DOI: https://doi.org/10.1007/s002110050411