Schur flow for orthogonal polynomials on the unit circle and its integrable discretization

被引：36

作者：

Mukaihira, A

Nakamura, Y

机构：

[1] Mitsubishi Res Inst Inc, Chiyoda Ku, Tokyo 1008141, Japan

[2] Osaka Univ, Grad Sch Engn Sci, Dept Informat & Math Sci, Toyonaka, Osaka 5608531, Japan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2002年 / 139卷 / 01期

基金：

日本学术振兴会;

关键词：

orthogonal polynomials on the unit circle; Schur flow; integrable discretization; Pade approximation; Perron-Caratheodory continued fraction;

D O I：

10.1016/S0377-0427(01)00388-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Pade approximation of the Caratheodory functions, or equivalently, to compute a Perron-Caratheodory continued fraction in. a polynomial time. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：75 / 94

页数：20

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