Fast parallel algorithms for QR and triangular factorization
SIAM Journal on Scientific and Statistical Computing
LAPACK's user's guide
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
Stability of fast algorithms for structured linear systems
Fast reliable algorithms for matrices with structure
MPI: The Complete Reference
Schur-Type Methods for Solving Least Squares Problems with Toeplitz Structure
SIAM Journal on Scientific Computing
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In this paper we present a parallel algorithm that solves the Toeplitz Least Squares Problem. We exploit the displacement structure of Toeplitz matrices and parallelize the Generalized Schur method. The stability problems of the method are solved by using a correction process based on the Corrected Semi-Normal Equations [10]. Other problems arising in the parallelization of the method, such as the data dependencies and high communication cost, have been addressed with an optimized distribution of the data, rearrangement of the computations, and with the design of new basic parallel subroutines. We have used standard tools like the ScaLAPACK library based on the MPI environment. Experimental results have been obtained in a cluster of personal computers with a high performance interconnection network.