Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement

Ondrej Slučiak, Hana Straková, Markus Rupp, Wilfried Gansterer

We present a novel distributed QR factorization algorithm for orthogonalizing a set of vectors in a decentralized wireless sensor network. The algorithm is based on the classical Gram-Schmidt orthogonalization with all projections and inner products reformulated in a recursive manner. In contrast to existing distributed orthogonalization algorithms, all elements of the resulting matrices Q and R are computed simultaneously and refined iteratively after each transmission. Thus, the algorithm allows a trade-off between run time and accuracy. Moreover, the number of transmitted messages is considerably smaller in comparison to state-of-the-art algorithms. We thoroughly study its numerical properties and performance from various aspects. We also investigate the algorithm's robustness to link failures and provide a comparison with existing distributed QR factorization algorithms in terms of communication cost and memory requirements.