Distributed Gram-Schmidt orthogonalization based on dynamic consensus

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.