ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Polynomial and Rational Eigenvalue Problems

Wed 12:00–12:30, Room AV 91.12
Some notes on the Birkhoff interpolation problem
Nikta Shayanfar (TU Braunschweig)
Joint work with Amir Amiraslani (University of Hawaii-Maui College); Heike Fassbender (TU Braunschweig)

We propose a new set of basis polynomials for representing the Birkhoff interpolation polynomial, which is an extension of the well-known Lagrange and Hermite interpolation problems. The proposed basis extends the definition of the Newton basis for non-distinct interpolation nodes. This approach allows to determine the Birkhoff interpolation polynomial via a special linear system of equations. When applied to the special cases of Taylor, Lagrange and Hermite interpolations, this approach reduces to the well-known solutions of these problems expressed in the Newton basis. Therefore, the characteristics of the Birkhoff basis can be exploited from Newton basis. In particular, the structure of the polynomial as well as companion matrices will be as straightforward as for Newton basis.