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Sparsity Analysis of QR Factorization

Every full column rank matrix has a unique factorization as a product of a matrix with orthogonal colums (Q) and an upper triangular matrix with positive diagonal (R), the famous QR factorization. When A is large and sparse, it is useful to know how sparse Q and R will be, for purposes of allocating storage in anticipation of calculation. It had been observed that Q (especially) tended in certain circumstances to be sparser than was easily predicted by the simple analysis then in use. We explain, based upon some subtlety of orthogonality, why this happens and give a description of the sparsity of Q and R. This is joint work with Pauline vanden Driessche and Dale Olesky.

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