What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Algorithms for computer algebra
Algorithms for computer algebra
Exact arithmetic at low cost—a case study in linear programming
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A method for cutting squares into distinct squares
Discrete Applied Mathematics
The Algebraic Solution of Sparse Linear Systems via Minor Expansion
ACM Transactions on Mathematical Software (TOMS)
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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.