Parallel Complexity of Householder QR Factorization

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.