Efficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes

Abstract

LU decomposition is intensively used in various scientific and engineering computations. A parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes is presented. Using n processors, the presented algorithm can finish LU decomposition of an n × n matrix in O( n 2 3 + O(n√n log 2 n)) steps, including computations as well as communications, and its efficiency is 1 asymptotically when n becomes large. The algorithm employs row- column- as well as block-parallelisms interchangeably so that the n processors are used efficiently in the whole computation process. Using the rich connectivity, all the data alignment requirements can be realized in O(log 2 n) steps. The algorithm proposed here not only is suitable for systems with small numbers of processors, but also is suitable for systems with large numbers of processors.