Fast parallel algorithms for QR and triangular factorization
SIAM Journal on Scientific and Statistical Computing
The WY representation for products of householder matrices
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
Hyperbolic Householder algorithms for factoring structured matrices
SIAM Journal on Matrix Analysis and Applications
Displacement structure: theory and applications
SIAM Review
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
IBM Journal of Research and Development
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An Efficient Parallel Algorithm to Solve Block-Toeplitz Systems
The Journal of Supercomputing
On Solving Block Toeplitz Systems Using a Block Schur Algorithm
ICPP '94 Proceedings of the 1994 International Conference on Parallel Processing - Volume 03
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There exist algorithms, also called "fast" algorithms, which exploit the special structure of Toeplitz matrices so that, e.g., allow to solve a linear system of equations in O(n 2) flops. However, some implementations of classical algorithms that do not use this structure (O(n 3) flops) highly reduce the time to solution when several cores are available. That is why it is necessary to work on "fast" algorithms so that they do not lose track of the benefits of new hardware/software. In this work, we propose a new approach to the Generalized Schur Algorithm, a very known algorithm for the solution of Toeplitz systems, to work on a Block---Toeplitz matrix. Our algorithm is based on matrix---matrix multiplications, thus allowing to exploit an efficient implementation of this operation if it exists. Our algorithm also makes use of the thread level parallelism featured by multicores to decrease execution time.