SPECTRA: solving linear matrix inequalities in exact arithmetic

Linear Matrix Inequalities (LMI) are a class of convex feasibility problems appearing in different applied contexts. For instance, checking the asymptotic stability for linear differential systems, or computing nonnegativity certificates for multivariate polynomials, are LMI. I will discuss an approach based on techniques from real algebraic geometry to compute exact solutions to LMI, and what information are carried by this representation. The related algorithms are implemented in a Maple library called SPECTRA, and part of the talk will be dedicated to discuss tests on interesting examples.