Optimum scaling of non-symmetric Jacobian matrices for threshold pivoting preconditioners

A new scaling method for non-symmetric matrices is presented. The scaling is based on purely mathematical considerations. It is highly adapted to the demands of incomplete LU factorization preconditioners with numerical dropping strategy. These preconditioners are the best state-of-the-art instruments for solving ill-conditioned linear systems with very large numbers of equations. The new scaling method causes a considerable improvement in the capabilities of these preconditioners, both in execution speed and robustness