title: Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement.
abstract: 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 matricesQandRare 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.
authors.affiliation: TU Wien, Institute of Telecommunications, Gusshausstrasse 25/E389, Vienna, 1040 Austria.
authors.forename: Ondrej
authors.initials: O
authors.lastname: Slučiak
authors.affiliation: University of Vienna, Faculty of Computer Science, Theory and Applications of Algorithms, Währingerstrasse 29, Vienna, 1090 Austria.
authors.forename: Hana
authors.initials: H
authors.lastname: Straková
authors.affiliation: TU Wien, Institute of Telecommunications, Gusshausstrasse 25/E389, Vienna, 1040 Austria.
authors.forename: Markus
authors.initials: M
authors.lastname: Rupp
authors.affiliation: University of Vienna, Faculty of Computer Science, Theory and Applications of Algorithms, Währingerstrasse 29, Vienna, 1090 Austria.
authors.forename: Wilfried
authors.initials: W
authors.lastname: Gansterer
keywords: Distributed processing; Gram-Schmidt orthogonalization; QR factorization