Effective Methods for Solving Banded Toeplitz Systems
Abstract
We propose new algorithms for solving n x n banded Toeplitz systems with bandwidth m. If the function associated with the Toeplitz matrix has no zero in the unit circle, then $O(n\log m + m\log ^2 m\log\log \epsilon^{-1})$ arithmetic operations (ops) are sufficient to approximate the solution of the system up to within the error $\epsilon$; otherwise the cost becomes $O(n\log m +m\log^2 m\log {n\over m})$ ops. Here $m=o(n)$ and $n>\log \epsilon^{-1}$. Some applications are presented. The methods can be applied to infinite and bi-infinite systems and to block matrices.
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SIAM Journal on Matrix Analysis and Applications
Pages: 700 - 719
ISSN (online): 1095-7162
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Copyright © 1999 Society for Industrial and Applied Mathematics.
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Published online: 31 July 2006
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