A deconvolution problem related to a singular system
type: Item
instance of: scholarly article
title: A deconvolution problem related to a singular system
zbMATH Open document ID: 1057.65101
author: Angelo Favini
author: Vyacheslav I. Maksimov
author: Luciano Pandolfi
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors derive a recursive algorithm for solving the deconvolution problem \[ y(t)= \int^t_0 H(t-s) u(s)\,ds,\quad t> 0, \] assuming that the impulse response function \(H\) is generated by the singular system \[ {d\over dt} (My)+ Ly= Bu,\quad My(0)= 0. \] Here, \(L\) and \(M\) are closed linear operators on a Hilbert space, with \(L\) possessing a bounded inverse. A change of variables (given by \(Ly= x\)) is used to formulate the identification problem in a \(C_0\)-semigroup framework. The resulting algorithm is in the spirit of the one introduced in \textit{Yu. S. Osipov} and \textit{A. V. Kryazhimskii} [Inverse problems for ordinary differential equations: dynamical solutions (Gordon and Breach, Amsterdam) (1995; Zbl 0884.34015)]; see also the recent papers by \textit{V. Maksimov} and \textit{L. Pandolfi} [J. Optimization Theory Appl. 103, No. 2, 401--420 (1999; Zbl 0956.49020)] and by the authors [SIAM J. Control Optimization 40, No. 5, 1384--1405 (2002; Zbl 1018.93016)] on related algorithms for distributed and finite-dimensional systems, respectively.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45Q05
zbMATH DE Number: 2081782
zbMATH Keywords: deconvolution
zbMATH Keywords: Volterra integral equations
zbMATH Keywords: singular systems
zbMATH Keywords: inverse problems
zbMATH Keywords: Hilbert space
zbMATH Keywords: identification problem
zbMATH Keywords: algorithm
reviewed by: H. Brunner
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.11.058
OpenAlex ID: W2002809812
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DOI: 10.1016/J.JMAA.2003.11.058
description: scientific article; zbMATH DE number 2081782