Which pivot to solve linear systems?

According to the specified goal, that is to say better numerical precision and/or better efficiency, we can select the most adapted method to solve linear systems of equations. As it exists several pivots which may guaranty a perfect result with the use of the floating-point unit, we were motivated by an exact calculation at low cost for our problem. We have compared all the alternatives and we present a panorama of the already available pivots with two improvements. Exact calculations instead of approximated ones have been implemented with 2% of runtime overcost in our example.