Discrete hungry integrable systems and new algorithms for computing matrix eigenvalues
- Speaker:
- Akiko Fukuda (guest of Kuniyoshi Abe)
- Date / time:
- Thursday 20 November 2008, 13:00
- Location:
- Geophysics (Aardwetenschappen) building, room C118
Abstract
The integrable discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra system which stands for a prey-predator model in mathematical biology. By using the dhLV system, we design a new algorithm for computing complex eigenvalues of a certain band matrix. On the other hand, it is known that the recursion formula of qd (quotient difference) algorithm for computing matrix eigenvalues is equivalent to the integrable discrete Toda equation.
As an extension of the discrete Toda equation, we derive a kind of discrete hungry Toda (dhToda) equation without the loss of integrability.By using the dhToda equation, we also design another algorithm for computing matrix eigenvalues like qd algorithm. Original qd algorithm has a possibility of numerical instability because its recursion formula has a subtraction. The recursion formula by using the dhToda equation also has a subtraction. Then we rewrite it to be numerically stable, along the similar way of deriving dqd (differential qd) algorithm, which is improvement of qd algorithm. In this talk, we discuss some relation between these hungry integrable systems and new algorithms for computing complex eigenvalues.