A discretization of the Schur flow and its applications
Yoshimasa Nakamura
Abstract:
The Schur flow is a deformation equation of the Schur parameter
which is induced by a linear evolution of measures for orthogonal
polynomials on the unit circle. The Schur flow is an integrable system
admitting a tau-function solution as well as a Lax representation.
In this talk I first give an integrable time discretization of the Schur
flow where the tau-function plays a central role. As applications of
the discrete Schur flow two algorithms are designed. One is a
continued fraction expansion algorithm of given power series.
The other is an algorithm for computing zeros of given polynomials.