What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Exact arithmetic at low cost—a case study in linear programming
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Certifying and repairing solutions to large LPs how good are LP-solvers?
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fast and Accurate Bounds on Linear Programs
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
On Using Floating-Point Computations to Help an Exact Linear Arithmetic Decision Procedure
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Solving Very Sparse Rational Systems of Equations
ACM Transactions on Mathematical Software (TOMS)
An exact rational mixed-integer programming solver
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Integration of an LP solver into interval constraint propagation
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Operations Research Letters
Exact solutions to linear programming problems
Operations Research Letters
Improving the accuracy of linear programming solvers with iterative refinement
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Valid Linear Programming Bounds for Exact Mixed-Integer Programming
INFORMS Journal on Computing
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With standard linear programming solvers there is always some uncertainty about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the exact optimal objective values for all NETLIB problems.