Vy. Pan et al., ALGEBRAIC AND NUMERICAL TECHNIQUES FOR THE COMPUTATION OF MATRIX DETERMINANTS, Computers & mathematics with applications, 34(1), 1997, pp. 43-70
We review, modify, and combine together several numerical and algebrai
c techniques in order to compute the determinant of a matrix or the si
gn of such a determinant. The resulting algorithms enable us to obtain
the solution by using a lower precision of computations and relativel
y few arithmetic operations. The problem has important applications to
computational geometry.