Gaussian Elimination with Partial Pivoting and Householder QRfactorization are two very popular methods to solve linear systems.Implementations of these two methods are provided in state-of-the-artnumerical libraries and packages, such as LAPACK and MATLAB.Gaussian Elimination with Partial Pivoting was already known to beP-complete. Here we prove that the Householder QR factorization islikely to be inherently sequential as well. We also investigate theproblem of speedup vs non degeneracy and accuracy in numericalalgorithms.
Parallel Complexity of Householder QR Factorization / Leoncini, Mauro; G., Manzini; L., Margara. - STAMPA. - 1136:(1996), pp. 290-301. (Intervento presentato al convegno 4th European Symposium on Algorithms tenutosi a Barcelona, Spain nel September 25-27, 1996).
Parallel Complexity of Householder QR Factorization
LEONCINI, Mauro;
1996
Abstract
Gaussian Elimination with Partial Pivoting and Householder QRfactorization are two very popular methods to solve linear systems.Implementations of these two methods are provided in state-of-the-artnumerical libraries and packages, such as LAPACK and MATLAB.Gaussian Elimination with Partial Pivoting was already known to beP-complete. Here we prove that the Householder QR factorization islikely to be inherently sequential as well. We also investigate theproblem of speedup vs non degeneracy and accuracy in numericalalgorithms.
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