Schur flow for orthogonal polynomials on the unit circle and its integrable discretization |
| |
Affiliation: | 1. Mitsubishi Research Institute, Inc., 3-6, Otemachi 2-chome, Chiyoda-ku, Tokyo 100-8141, Japan;2. Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Machikaneyama-cho 1-3, Toyonaka, Osaka 560-8531, Japan |
| |
Abstract: | A one-parameter deformation of the measure of orthogonality for orthogonal polynomials on the unit circle is considered. The corresponding dynamics of the Schur parameters of the orthogonal polynomials is shown to be characterized by the complex semi-discrete modified KdV equation, namely, the Schur flow. A discrete analogue of the Miura transformation is found. An integrable discretization of the Schur flow enables us to compute a Padé approximation of the Carathéodory functions, or equivalently, to compute a Perron–Carathéodory continued fraction in a polynomial time. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|