Pipeline Givens sequences for computing the QR decomposition on a EREW PRAM
Parallel Computing
Computationally efficient methods for estimating the updated-observations SUR models
Applied Numerical Mathematics
A graph approach to generate all possible regression submodels
Computational Statistics & Data Analysis
Message-passing two steps least square algorithms for simultaneous equations models
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Two-stage least squares and indirect least squares algorithms for simultaneous equations models
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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The QR decomposition of a set of matrices which have common columns is investigated. The triangular factors of the QR decompositions are represented as nodes of a weighted directed graph. An edge between two nodes exists if and only if the columns of one of the matrices is a subset of the columns of the other. The weight of an edge denotes the computational complexity of deriving the triangular factor of the destination node from that of the source node. The problem is equivalent to constructing the graph and finding the minimum cost for visiting all the nodes. An algorithm which computes the QR decompositions by deriving the minimum spanning tree of the graph is proposed. Theoretical measures of complexity are derived and numerical results from the implementation of this and alternative heuristic algorithms are given.