{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T07:27:51Z","timestamp":1772350071088,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100002261","name":"RFBR","doi-asserted-by":"crossref","award":["15-01-09230"],"award-info":[{"award-number":["15-01-09230"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003443","name":"Ministry of Education and Science of the Russian Federation","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002261","name":"RFBR","doi-asserted-by":"crossref","award":["15-01-00977"],"award-info":[{"award-number":["15-01-00977"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004561","name":"Ministry of Education and Science of the Republic of Kazakhstan","doi-asserted-by":"crossref","award":["1746\/GF \u201cTheory and numerical methods for solving inverse and ill-posed\nproblems of natural sciences\u201d"],"award-info":[{"award-number":["1746\/GF \u201cTheory and numerical methods for solving inverse and ill-posed\nproblems of natural sciences\u201d"]}],"id":[{"id":"10.13039\/501100004561","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>An inverse problem of reconstructing the two-dimensional coefficient of the wave equation is solved by a stochastic projection method. We apply the Gel'fand\u2013Levitan approach to reduce the nonlinear inverse problem to a family of linear integral equations. The stochastic projection method is applied to solve the relevant linear system. We analyze the structure of the problem to increase the efficiency of the method by constructing an improved initial approximation. A smoothing spline is used to treat the random errors of the method. The method has low cost and memory requirements. Results of numerical calculations are presented.<\/jats:p>","DOI":"10.1515\/mcma-2015-0103","type":"journal-article","created":{"date-parts":[[2015,7,15]],"date-time":"2015-07-15T17:21:28Z","timestamp":1436980888000},"page":"189-203","source":"Crossref","is-referenced-by-count":20,"title":["Numerical solution of an inverse problem of coefficient recovering for\na wave equation by a stochastic projection methods"],"prefix":"10.1515","volume":"21","author":[{"given":"Sergey I.","family":"Kabanikhin","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl K.","family":"Sabelfeld","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikita S.","family":"Novikov","sequence":"additional","affiliation":[{"name":"Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maxim A.","family":"Shishlenin","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics SB RAS, Akad. Koptyug avenue, 4, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2015,7,15]]},"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2015-0103\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2015-0103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T22:40:03Z","timestamp":1680388803000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2015-0103\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,15]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,9,1]]},"published-print":{"date-parts":[[2015,9,1]]}},"alternative-id":["10.1515\/mcma-2015-0103"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2015-0103","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,15]]}}}