Matrix Equations and Structures: Efficient Solution of Special Discrete Algebraic Riccati Equations
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Skew-Circulant Preconditioners for Systems of LMF-Based ODE Codes
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Superlinear convergence for PCG using band plus algebra preconditioners for Toeplitz systems
Computers & Mathematics with Applications
A direct method to solve block banded block Toeplitz systems with non-banded Toeplitz blocks
Journal of Computational and Applied Mathematics
A probabilistic algorithm for determining the fundamental matrix of a block M/G/1 markov chain
Mathematical and Computer Modelling: An International Journal
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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.