The method can also be used to compute the determinant of matrices with (approximated) real entries, avoiding the introduction of any round-off errors beyond those already present in the input.
In some Spanish-speaking countries, this algorithm is also known as Bareiss-Montante, because of René Mario Montante Pardo, a professor of the Universidad Autónoma de Nuevo León, Mexico, who popularized the method among his students.
Gaussian elimination has O(n3) complexity, but introduces division, which results in round-off errors when implemented using floating point numbers.
[1] Bareiss brings up a question of performing an integer-preserving elimination while keeping the magnitudes of the intermediate coefficients reasonably small.
Otherwise, the Bareiss algorithm may be viewed as a variant of Gaussian elimination and needs roughly the same number of arithmetic operations.