We review, modify, and combine together several numerical and algebraic techniques in order to compute the determinant of a matrix or the sign of such a determinant. The resulting algorithms enable us to obtain the solution by using a lower precision of computations and relatively few arithmetic operations. The problem has important applications to computational geometry.
Pan, V. Y., Yu, Y., & Stewart, C. (1997). Algebraic and numerical techniques for the computation of matrix determinants. Computers and Mathematics with Applications, 34(1), 43–70. https://doi.org/10.1016/S0898-1221(97)00097-7