Inequalities and asymptotics for Riccati matrix difference operators
type: Item
instance of: scholarly article
title: Inequalities and asymptotics for Riccati matrix difference operators
zbMATH Open document ID: 0914.39012
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-06-21T00:00:00Z
review text: Inequalities for the solutions of the Riccati matrix difference equation \[ Q_{k+1}= C_k+(I-A_k^T) Q_k(I+B_kQ_k)^{-1} (I-A_k) \] which correspond to the linear Hamiltonian difference system are developed. Finally the asymptotic behaviour of solutions \(Q_k(\lambda)\), as \(|\lambda|\to \infty\), of the special Riccati matrix difference equation is established which corresponds to the Sturm-Liouville equation \[ \sum_{\mu=0}^n (-1)^\mu r_\mu \Delta^{2\mu} y_{k+1-\mu}= \lambda y_{k+1} \] of even order \(2n\) with constant coefficients \(r_0,\dots, r_n\).
reviewed by: B. M. Agrawal
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 1215649
zbMATH Keywords: inequalities
zbMATH Keywords: Riccati matrix difference equation
zbMATH Keywords: linear Hamiltonian difference system
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Sturm-Liouville equation
author: Martin Bohner
author: Ondřej Došlý
author: Werner Kratz
MaRDI profile type: Publication
OpenAlex ID: W1968711661
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DOI: 10.1006/JMAA.1997.5890
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description: scientific article; zbMATH DE number 1215649