Displacement structure: theory and applications
SIAM Review
ScaLAPACK user's guide
A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations
SIAM Journal on Matrix Analysis and Applications
High-performance algorithms to solve toeplitz and block toeplitz matrices
High-performance algorithms to solve toeplitz and block toeplitz matrices
On Solving Block Toeplitz Systems Using a Block Schur Algorithm
ICPP '94 Proceedings of the 1994 International Conference on Parallel Processing - Volume 03
FFT algorithms for vector computers
Parallel Computing
An efficient parallel solution of complex toeplitz linear systems,
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
A parallel solution of hermitian toeplitz linear systems,
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
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In this paper, we parallelize a new algorithm for solving non-symmetric Toeplitz linear systems. This algorithm embeds the Toeplitz matrix in a larger structured matrix, then transforms it into an embedded Cauchy-like matrix by means of trigonometric modifications. Finally, the algorithm applies a modified QR transformation to triangularize the augmented matrix. The algorithm combines e.ciency and stability. It has been implemented using standard tools and libraries, thereby producing a portable code. An extensive experimental analysis has been performed on a cluster of personal computers. Experimental results show that we can obtain efficiencies that are similar to other fast parallel algorithms, while obtaining more accurate results with only one iterative refinement step in the solution.