Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation 2013
DOI: 10.1145/2465506.2465517
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Simultaneous computation of the row and column rank profiles

Abstract: International audienceGaussian elimination with full pivoting generates a PLUQ matrix decomposition. Depending on the strategy used in the search for pivots, the permutation matrices can reveal some information about the row or the column rank profiles of the matrix. We propose a new pivoting strategy that makes it possible to recover at the same time both row and column rank profiles of the input matrix and of any of its leading sub-matrices. We propose a rank-sensitive and quad-recursive algorithm that compu… Show more

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Cited by 17 publications
(43 citation statements)
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“…Although this computation has already been widely studied for numerical computation [8], applications over a finite field have additional specific requirements and constraints that need to be taken into consideration. In particular, rank deficiency is a well defined notion there, and many applications rely on the computation of the echelon form, or the rank profile of the matrix [21,13] only revealed by certain pivoting strategies in the PLUQ factorization algorithm.…”
Section: Parallel Gaussian Eliminationmentioning
confidence: 99%
See 2 more Smart Citations
“…Although this computation has already been widely studied for numerical computation [8], applications over a finite field have additional specific requirements and constraints that need to be taken into consideration. In particular, rank deficiency is a well defined notion there, and many applications rely on the computation of the echelon form, or the rank profile of the matrix [21,13] only revealed by certain pivoting strategies in the PLUQ factorization algorithm.…”
Section: Parallel Gaussian Eliminationmentioning
confidence: 99%
“…Such an iterative algorithm can be translated into a slab recursive algorithm splitting the row dimension in halves (as implemented in sequential in [12]) or into a slab iterative algorithm. More recently, a more flexible pivoting strategy that results in a tile recursive algorithm, cutting both dimensions simultaneously was presented in [13,14]. As a by product, both row and column rank profiles are also computed simultaneously.…”
Section: Algorithmic Variants For Pluq Factorizationmentioning
confidence: 99%
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“…In particular, the PLUQ decomposition algorithm of Dumas et al (2013) computes the rank profile matrix of A in O(n 2 r ω−2 ) where r = rank(A). However this estimate may be pessimistic as it does not take into account the left triangular shape of the matrix.…”
Section: From a Pluq Decompositionmentioning
confidence: 99%
“…In order to reach a complexity depending on s and not r, we adapt in Algorithm 2 the tile recursive algorithm of Dumas et al (2013), so that the left triangular structure of the input matrix is preserved and can be used to reduce the amount of computation.…”
Section: A Dedicated Algorithmmentioning
confidence: 99%