Projects
Wronskian polynomials and determinantal point processes KU Leuven
This thesis consists of two parts. In the first part, we develop a combinatorial framework for studying Wronskians of polynomials and we exploit this framework to find relations between such polynomials. Our main results include several recurrence relations, averaging results and derivative properties. We show that for Wronskian Appell polynomials these results are closely related to symmetric function theory. For the specific case of ...
Orthogonal Polynomials and Matrix Computations. Applications of Recurrence Relations. KU Leuven
Univariate and multivariate polynomials play a fundamental role in pure and applied mathematics.
In this text orthogonal polynomials and their corresponding recurrence relations are studied
and connected to matrix computations
and applied in polynomial interpolation and approximation and in polynomial system solving.
For univariate orthogonal polynomials on the complex unit circle, efficient algorithms for ...
Solving Systems of Polynomial Equations KU Leuven
Systems of polynomial equations arise naturally from many problems in applied mathematics and engineering. Examples of such problems come from robotics, chemical engineering, computer vision, dynamical systems theory, signal processing and geometric modeling, among others. The numerical solution of systems of polynomial equations is considered a challenging problem in computational mathematics. Important classes of existing methods are ...