Seminar Details
2018-02-20 (14:00) : Back to the roots: Multivariate polynomial optimization by numerical linear algebra
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Bart De Moor (KU Leuven)
Abstract :
Finding some or all of the roots of a set of multivariate polynomials has numerous applications. This century old problem is at the foundation of algebraic geometry sometimes called the 'queen of mathematics'. In this discipline, typically, numerical computations are done symbolically, and only quite recently, it was realized that the multivariate polynomial rooting problem can be tackled using the machinery of numerical linear algebra, because of the fundamental insight that it is equivalent to an eigenvalue problem. In order to find some or all roots, we deploy tools like the QR- and singular value decomposition, and (possibly large scale) iterative eigenvalue solvers. We will discuss several eigenvalue decomposition based algorithms to calculate the global minimum of multivariate polynomial optimization problems. We will illustrate our approach with the numerical solution of two open problems in system theory: Calculating from (noisy) data linear dynamic models that are least squares optimal, and finding the least squares global optimum of the H2 model reduction problem.