<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations in problems data.</p></abstract>

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations in problems data.

On one algorithm for solving the problem of source function reconstruction

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskoi Str., Ekaterinburg, 620219 Russia

International Journal of Applied Mathematics and Computer Science

{"article-title":"On one algorithm for solving the problem of source function reconstruction"}

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup...

On one algorithm for solving the problem of source function reconstruction

Published Online: Jul 02, 2010

Page range: 239 - 247

DOI: https://doi.org/10.2478/v10006-010-0017-3

Keywords
reconstruction, source function, feedback control

This content is open access.

On one algorithm for solving the problem of source function reconstruction

Published Online: Jul 02, 2010

Page range: 239 - 247

DOI: https://doi.org/10.2478/v10006-010-0017-3

Keywordsreconstruction, source function, feedback control

This content is open access.

Keywords
reconstruction, source function, feedback control