DSF chain for biorthogonal polynomials and its application to matrix eigenvalue problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:347

Article

Mukaihira, Atsushi¹  Tsuboi, Yoshimasa¹ 

[1] Doshisha Univ, Fac Sci & Engn, Kyotanabe, Kyoto, Japan

关键词: Schur flow;    Qd-algorithm;    Matrix eigenvalue problems;    Numerical algorithms;    Integrable systems;    Biorthogonal polynomials;   

DOI  :  10.1016/j.cam.2018.03.023

来源: Elsevier

【 摘 要 】

A discrete-time integrable system, called the DSF chain, is derived from the compatibility condition of spectral equations for biorthogonal polynomials associated with the discrete Schur flow. The DSF algorithm for computing eigenvalues of a type of matrix eigenvalue problem is designed. A discrete analogue of the Miura transformation between the discrete Schur flow and the qd-algorithm is constructed. Two special solutions to the DSF chain related to q-special functions are presented. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free