Series of Lectures and Exercises: Order Bases: Applications and Computation

Date: 29/07/2019
Time: 00:00 - 00:00


Abstract: Order Bases takes as input a vector or matrix of power series F and describes all solutions (as a module) for approximation problems of the form F p = O(zω) with ω a scalar or a vector. These approximation problems date back to the work of Hermite and his student Padé and later contributions for Order bases were given by Mahler. More recently applications of Order bases to problems in Combinatorics have appeared through the work of Salvy and Bostan. In these lectures we give the history (basically coming from rational approximation and interpolation problems), fast algorithms for computation and applications. The applications will include fast computation of problems with matrix polynomial arithmetic, matrix normal forms in addition to the problems arising in Combinatorics.