A Parallel Factorization for Generating Orthogonal Matrices
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A new factorization of orthogonal matrices is proposed that is based on Givens-Jacobi rotations but not on the QR decomposition. Rotations are arranged more uniformly than in the known factorizations that use them, so that more rotations can be computed in parallel, and fewer layers of concurrent rotations are necessary to model a matrix. Therefore, throughput can be increased, and latency can be reduced, compared to the known solutions, even though the obtainable gains highly depend on application specificity, software-hardware architecture and matrix size. The proposed approach allows for developing more efficient algorithms and hardware for generating random matrices, for optimizing matrices, and for processing data with linear transformations. We have verified this by implementing and evaluating a multithreaded Java application for generating random orthogonal matrices.
KeywordsMatrix Orthogonal Rotation Factorization Parallel
This work was financially supported from the Polish Ministry of Science and Higher Education under subsidy for maintaining the research potential of the Faculty of Mathematics and Informatics, University of Bialystok.
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