A parallel algorithm for incremental orthogonalization based on the compact WY representation

Abstract

We present a parallel algorithm for incremental orthogonalization, where the vectors to be orthogonalized are given one by one at each step. It is based on the compact WY representation and always produces vectors that are orthogonal to working accuracy. Moreover, it has large granularity and can be parallelized efficiently. When applied to the GMRES method, this algorithm reduces to a known algorithm by Walker. However, our formulation makes it possible to apply the algorithm to a wider class of incremental orthogonalization problems, as well as to analyze its accuracy theoretically. Numerical experiments demonstrate accuracy and scalability of the algorithm.