# On one algorithm for solving the problem of source function reconstruction

International Journal of Applied Mathematics and Computer Science (2010)

- Volume: 20, Issue: 2, page 239-247
- ISSN: 1641-876X

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topVyacheslav Maksimov. "On one algorithm for solving the problem of source function reconstruction." International Journal of Applied Mathematics and Computer Science 20.2 (2010): 239-247. <http://eudml.org/doc/207983>.

@article{VyacheslavMaksimov2010,

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.},

author = {Vyacheslav Maksimov},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {reconstruction; source function; feedback control},

language = {eng},

number = {2},

pages = {239-247},

title = {On one algorithm for solving the problem of source function reconstruction},

url = {http://eudml.org/doc/207983},

volume = {20},

year = {2010},

}

TY - JOUR

AU - Vyacheslav Maksimov

TI - On one algorithm for solving the problem of source function reconstruction

JO - International Journal of Applied Mathematics and Computer Science

PY - 2010

VL - 20

IS - 2

SP - 239

EP - 247

AB - 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.

LA - eng

KW - reconstruction; source function; feedback control

UR - http://eudml.org/doc/207983

ER -

## References

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- Kryazhimskii, A.V. and Osipov, Yu.S. (1987). To a regularization of a convex extremal problem with inaccurately given constraints. An application to an optimal control problem with state constraints, in A.I. Korotkii and V.I. Maksimov (Eds.), Some Methods of Positional and Program Control, Ural Scientific Center, Sverdlovsk, pp. 34-54, (in Russian).
- Omatu, S. and Seinfeld, J. (1989). Distributed Parameter Systems: Theory and Applications, Oxford Mathematical Monographs, Oxford University Press, New York, NY. Zbl0675.93001
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