Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems
Numerische Mathematik
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Matrix computations (3rd ed.)
Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices
SIAM Journal on Matrix Analysis and Applications
Effective Methods for Solving Banded Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications
A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications
A fast algorithm for Toeplitz-block-Toeplitz linear systems
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 03
A fast algorithm for the inversion of general Toeplitz matrices
Computers & Mathematics with Applications
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A fast solution algorithm is proposed for solving block banded block Toeplitz systems with non-banded Toeplitz blocks. The algorithm constructs the circulant transformation of a given Toeplitz system and then by means of the Sherman-Morrison-Woodbury formula transforms its inverse to an inverse of the original matrix. The block circulant matrix with Toeplitz blocks is converted to a block diagonal matrix with Toeplitz blocks, and the resulting Toeplitz systems are solved by means of a fast Toeplitz solver. The computational complexity in the case one uses fast Toeplitz solvers is equal to @x(m,n,k)=O(mn^3)+O(k^3n^3) flops, there are m block rows and m block columns in the matrix, n is the order of blocks, 2k+1 is the bandwidth. The validity of the approach is illustrated by numerical experiments.