Posted by Paul on September 09, 1998 at 04:57:37:
In Reply to: Solving det(A) = 0 posted by Chris on June 17, 1998 at 10:43:27:
: As a part of a system of nonlinear equations, one function to be solved is det(A) = 0, where the elements of the matrix A are indirectly dependent on the vector of unknowns. My problem is that for poor initial guesses det(A) is quite large(10^30) and continuing a numerical method until there is no change in the unknowns (i.e., below machine precision) reduces det(A) only to 10^15 (which is still quite far from zero). Does anybody know of a way to scale A (or know of an equivalent solution to det(A) = 0) that will give a more accurate solution? Currently, different initial guesses and numerical methods will continue until there is no change in the unknowns, but the "solution" is different for each case (within approx. 20% of each other, though).
Use instead of det(A) the smallest singular value as a measure for singularity.
Before, scale the matrix.
I think this should be work.