Matrix Hermite-Padé problem and dynamical systems
type: Item
instance of: scholarly article
title: Matrix Hermite-Padé problem and dynamical systems
zbMATH Open document ID: 0984.37023
DOI: 10.1016/S0377-0427(00)00354-X
author: Jeannette Van Iseghem
author: V. N. Sorokin
published in: Journal of Computational and Applied Mathematics
publication date: 2002-05-01T00:00:00Z
review text: Consider the system \[ \begin{aligned} b_{n+3} &= b_{n+3}(U_{n+ 3}- U_{n- 2}),\\ U_{n+3} &= b_{n+ 6}(b_{n+ 9}+ b_{n+ 7}+ b_{n+ 5})+ b_{n+ 4}(b_{n+ 7}+ b_{n+ 5})+ b_{n+ 2} b_{n+5}\end{aligned} \] with \(b_{n+3}\equiv 0\), \(n< 0\). The authors consider the Cauchy problem with initial conditions \(b_{n+3}(0)\), \(n\geq 0\). Such systems arise from discrete generalizations of the KdV equation. A representation formula for the solution is given in terms of a matrix continued fraction and a spectral measure. The authors then study the associated Padé-Hermité problem and the differential equation satisfied by the moments of the spectral measure.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 37C30
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1548086
zbMATH Keywords: Hermité-Padé approximation
zbMATH Keywords: KdV equation
zbMATH Keywords: matrix continued fraction
zbMATH Keywords: spectral measure
MaRDI profile type: Publication
cites work: The genetic sums' representation for the moments of a system of Stieltjes functions and its application
cites work: Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions
cites work: SOME CONSTRUCTIONS OF INTEGRABLE DYNAMICAL SYSTEMS
cites work: INTEGRABLE DYNAMICAL SYSTEMS ASSOCIATED WITH THE KdV EQUATION
cites work: The interruption phenomenon for generalized continued fractions
cites work: Three integrable Hamiltonian systems connected with isospectral deformations
cites work: Q4001531
cites work: THE JACOBI-PERRON ALGORITHM AND SIMULTANEOUS APPROXIMATION OF FUNCTIONS
cites work: Completely integrable nonlinear dynamical systems of the Langmuir chains type
cites work: Algebraic aspects of matrix orthogonality for vector polynomials
cites work: Matrix continued fractions
cites work: Q4945661
cites work: Q5792555
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description: scientific article; zbMATH DE number 1548086