A modified Markowitz criterion for the fast modes of the LU factorization

A novel modification of the Markowitz criterion is suggested which is compatible with the fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities for all the column elements. Finally, the columns are reordered so that first and last should be those with the minimum and maximum probabilities, respectively. As a verification of the proposed algorithm, a comprehensive set of numerical tests is described for circuits chosen from various parts of electronics. Special attention is given to testing the radio frequency and microwave circuits