Elias Tsigaridas (Polsys) : Algebraic Algorithms: The era of computational non-linear algebra
Algebraic algorithms provide the research community with extremely powerful tools for computing with the solution set of polynomials in many variables. These tools allow us, on the one hand, to tackle theoretical problems involving non-linear objects, and on the other to produce efficient implementations. The mixture of algebraic algorithms with symbolic-numeric techniques and dedicated tools that exploit the geometry and the structure of the problem at hand,has enabled researchers to solve problems that were impossible in the past.
In this context we present the algebraic tools for computing the Voronoi diagram of ellipses in non-linear computational geometry, to obtain an algorithm for decomposing a tensor as a sum of rank one tensors, to compute the equilibrium of stochastic games, and to study the central curve that the interior point methods follow to solve semi-definite programs.