Title: Triangular Decomposition of Matrices in a Domain,
Abstract: Deterministic recursive algorithms for the computation of matrix triangular
decompositions with permutations like LU and Bruhat decomposition are presented
for the case of commutative domains. This decomposition can be considered as a
generalization of LU and Bruhat decompositions, because they both may be easily
obtained from this triangular decomposition. Algorithms have the same
complexity as the algorithm of matrix multiplication.