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O. Sluciak, H. Straková, M. Rupp, W. Gansterer:
"Distributed Gram-Schmidt Orthogonalization based on Dynamic Consensus";
Talk: Asilomar Conference on Signals, Systems, and Computers, Asilomar, Pacific Grove, CA, USA; 2012-11-04 - 2012-11-07; in: "Proceedings of the Asilomar SSC", (2012).

We propose a novel distributed QR factorization
algorithm for orthogonalizing a set of vectors in a wireless
sensor network. The algorithm originates from the classical Gram-
Schmidt orthogonalization which we formulate in a distributed
way using the dynamic consensus algorithm. In contrast to existing
distributed QR factorization algorithms, all elements of matrices Q
and R are computed simultaneously and updated iteratively after
each transmission. Assuming synchronous message broadcasting
and communication only with neighboring nodes without any
central computing unit (fusion center), we prove convergence
of the algorithm. We investigate the algorithm in terms of
numerical accuracy and we discuss the influence of the initial
data distribution on the algorithm performance. Moreover, we
provide a comparison with existing distributed QR algorithms in
terms of communication cost and memory requirements, and we
illustrate the comparison by simulations.

distributed algorithms, Gram-Schmidt orthogonalization, QR factorization, dynamic consensus algorithm, wireless sensor network

http://publik.tuwien.ac.at/files/PubDat_211005.pdf