# Matrix factoring by fraction-free reduction

@article{Middeke2016MatrixFB, title={Matrix factoring by fraction-free reduction}, author={Johannes Middeke and David J. Jeffrey}, journal={ArXiv}, year={2016}, volume={abs/1603.03565} }

We consider exact matrix decomposition by Gauss-Bareiss reduction. We investigate two aspects of the process: common row and column factors and the influence of pivoting strategies. We identify two types of common factors: systematic and statistical. Systematic factors depend on the process, while statistical factors depend on the specific data. We show that existing fraction-free QR (Gram-Schmidt) algorithms create a common factor in the last column of Q. We relate the existence of row factors…

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