Subtropical Real Root Finding

Thomas Sturm
2015 Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15  
We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method
more » ... ion of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases.
doi:10.1145/2755996.2756677 dblp:conf/issac/Sturm15 fatcat:tpwax5kxm5hxbejddd2z7gaok4