{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:44:21Z","timestamp":1709203461731},"reference-count":10,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,6,1]]},"abstract":"<jats:title>On one algorithm for solving the problem of source function reconstruction<\/jats:title><jats: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.<\/jats:p>","DOI":"10.2478\/v10006-010-0017-3","type":"journal-article","created":{"date-parts":[[2010,7,3]],"date-time":"2010-07-03T06:34:38Z","timestamp":1278138878000},"page":"239-247","source":"Crossref","is-referenced-by-count":2,"title":["On one algorithm for solving the problem of source function reconstruction"],"prefix":"10.61822","volume":"20","author":[{"given":"Vyacheslav","family":"Maksimov","sequence":"first","affiliation":[]}],"member":"37438","reference":[{"key":"1","volume-title":"Representation and Control of Infinite Dimensional Systems, Vol. I","author":"A. Bensoussan","year":"1992"},{"issue":"4","key":"2","first-page":"51","article-title":"On the reconstruction of an extremal input in a system with hereditary","volume":"4","author":"M. Blizorukova","year":"1998","journal-title":"Vestnik PGTU. Matematika i Prikladnaya Matematika (Mathematics and Applied Mathematics)"},{"key":"3","first-page":"84","volume-title":"Computational Seismology and Geodynamics","author":"B. Digas","year":"2003"},{"key":"4","volume-title":"Estimation and Control of Stochastic Distributed-Parameter Systems","author":"J. Korbicz","year":"1991"},{"key":"5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3716-7","volume-title":"Game-Theoretical Control Problems","author":"N. Krasovskii","year":"1988"},{"issue":"3","key":"6","first-page":"119","article-title":"Reconstruction of extremal disturbances in parabolic equations","volume":"37","author":"A. Kryazhimskii","year":"1997","journal-title":"Journal of Computational Mathematics and Mathematical Physics"},{"key":"7","first-page":"34","volume-title":"Some Methods of Positional and Program Control","author":"A. Kryazhimskii","year":"1987"},{"key":"8","volume-title":"Distributed Parameter Systems: Theory and Applications","author":"S. Omatu","year":"1989"},{"key":"9","volume-title":"Measurement Optimization for Parameter Estimation in Distributed Systems","author":"D. Uci\u0144ski","year":"1999"},{"key":"10","volume-title":"Solution Methods to Extremal Problems","author":"F. Vasiliev","year":"1981"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/20\/2\/article-p239.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2010.20.issue-2\/v10006-010-0017-3\/v10006-010-0017-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:27:46Z","timestamp":1709202466000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-010-0017-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,1]]},"references-count":10,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/v10006-010-0017-3","relation":{},"ISSN":["1641-876X"],"issn-type":[{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2010,6,1]]}}}