Geodesic
The sparsity of Bruhat decomposition factors of nonsingular matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part IX, Tome 202 (1992), pp. 5-17 
L. Yu. Kolotilina. The sparsity of Bruhat decomposition factors of nonsingular matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part IX, Tome 202 (1992), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_1992_202_a0/
@article{ZNSL_1992_202_a0,
     author = {L. Yu. Kolotilina},
     title = {The sparsity of {Bruhat} decomposition factors of nonsingular matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--17},
     year = {1992},
     volume = {202},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_202_a0/}
}
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The paper analyzes the sparsity pattern of triangular factors of the reduced Bruhat decomposition of a non-singular matrix over a field, which is an alternative to the commonly used LU decomposition. Bounds for the length of the Bruhat permutation of a matrix providing upper bounds for the number of nonzero entries in the reduced triagular factor of its Bruhat decomposition are also presented. Bibliography: 6 titles.