Abstract
A particular class of preconditioners for the conjugate gradient method and other iterative methods is proposed for the solution of linear systemsAn,mx=b, whereAn,m is ann×n positive definite block Toeplitz matrix withm×m Toeplitz blocks. In particular we propose a sparse preconditionerPn,m such that the condition number of the preconditioned matrix turns out to be less than a suitable constant independent of bothn andm, even if the condition number ofAn,m tends to ∞. This leads to iterative methods which require a number of steps independent ofm andn in order to reduce the error by a given factor.
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