LU factorization on parallel computers (Q1067753)

A new parallel algorithm for the LU factorization of a given dense matrix A is described. The case of banded matrices is also considered. This algorithm can be combined with the algorithm of \textit{A. H. Sameh} and \textit{R. P. Brent} [SIAM J. Numer. Anal. 14, 1101-1113, (1977; Zbl 0375.65016)] to obtain the solution of a linear system of algebraic equations. The arithmetic complexity for the dense case is \((1/3)n^ 2\) ((1/2)bn in the banded case), using 3(n-1) processors and no square roots.