The accuracy of a parallel \(LU\) decomposition algorithm (Q920567)

An error analysis for a parallel \(LU\) decomposition algorithm which was proposed by \textit{B. Neta} and \textit{H.-M. Tai} [ibid. 11, 573--579 (1986; Zbl 0581.65019)] is given. The author defines two error complexity measures and compares the usual sequential \(LU\) decomposition algorithm with the parallel algorithm based on these error measures. This comparison shows that for large-dimensioned systems of equations both algorithms are practically equivalent, but for systems with only few equations the parallel algorithm is slightly inferior to the standard \(LU\) decomposition algorithm. That is also demonstrated by numerical examples.