Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Fast Gaussian elimination with partial pivoting for matrices with displacement structure
Mathematics of Computation
Displacement structure: theory and applications
SIAM Review
ScaLAPACK user's guide
Transformation Techniques for Toeplitz and Toeplitz-plus-Hankel Matrices Part I. Transformations
Transformation Techniques for Toeplitz and Toeplitz-plus-Hankel Matrices Part I. Transformations
Transformation Techniques for Toeplitz and Toeplitz-plus-Hankel Matrices Part II. Algorithms
Transformation Techniques for Toeplitz and Toeplitz-plus-Hankel Matrices Part II. Algorithms
High-performance algorithms to solve toeplitz and block toeplitz matrices
High-performance algorithms to solve toeplitz and block toeplitz matrices
FFT algorithms for vector computers
Parallel Computing
An efficient and stable parallel solution for non-symmetric toeplitz linear systems
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
The symmetric–toeplitz linear system problem in parallel
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
An adaptive interface for the efficient computation of the discrete sine transform
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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A parallel algorithm for solving complex hermitian Toeplitz linear systems is presented. The parallel algorithm exploits the special structure of Toeplitz matrices to obtain the solution in a quadratic asymptotical cost. Our parallel algorithm transfors the Toeplitz matrix into a Cauchy–like matrix. Working on a Cauchy–like system lets to work with real arithmetic. The parallel algorithm for the solution of a Cauchy–like matrix has a low amount of communication cost regarding other parallel algorithms that work directly on the Toeplitz system. We use a message–passing programming model. The experimental tests are obtained in a cluster of personal computers.