Estimate of error of an approximated solution by the method of moments of an operator equation
For an equationAu = f whereA is a closed densely defined operator in a Hilbert spaceH, f εH, we estimate the deviation of its approximated solution obtained by the moment method from the exact solution. All presented theorems are of direct and inverse character. The paper refers to direct methods of...
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| Date: | 1996 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5201 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511408190390272 |
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| author | Gorbachuk, M. L. Yakymiv, R. Ya. Горбачук, М. Л. Якимів, Р. Я. |
| author_facet | Gorbachuk, M. L. Yakymiv, R. Ya. Горбачук, М. Л. Якимів, Р. Я. |
| author_sort | Gorbachuk, M. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:27:04Z |
| description | For an equationAu = f whereA is a closed densely defined operator in a Hilbert spaceH, f εH, we estimate the deviation of its approximated solution obtained by the moment method from the exact solution. All presented theorems are of direct and inverse character. The paper refers to direct methods of mathematical physics, the development of which was promoted by Yu. D. Sokolov, the well-known Ukrainian mathematician and mechanic, a great humanitarian and righteous man. We dedicate this paper to his blessed memory. |
| first_indexed | 2026-03-24T03:12:25Z |
| format | Article |
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| id | umjimathkievua-article-5201 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:12:25Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a7/4767a8f93e5401cb3afe3379185f8aa7.pdf |
| spelling | umjimathkievua-article-52012020-03-18T21:27:04Z Estimate of error of an approximated solution by the method of moments of an operator equation Оцінка похибки наближеного розв'язку операторного рівняння методом моментів Gorbachuk, M. L. Yakymiv, R. Ya. Горбачук, М. Л. Якимів, Р. Я. For an equationAu = f whereA is a closed densely defined operator in a Hilbert spaceH, f εH, we estimate the deviation of its approximated solution obtained by the moment method from the exact solution. All presented theorems are of direct and inverse character. The paper refers to direct methods of mathematical physics, the development of which was promoted by Yu. D. Sokolov, the well-known Ukrainian mathematician and mechanic, a great humanitarian and righteous man. We dedicate this paper to his blessed memory. Для операторного рівняння $Au = f$ де $A$ — щільно заданий замкнений оператор у гільбертовому просторі $H\; f \in H$, встановлюються оцінки відхилення наближеного методом моментів розв'язку від його точного розв'язку. Наведені теореми носять прямий і обернений характер. Результати пов'язані з прямими методами математичної фізики, розвиткові яких всіляко сприяв Ю. Д. Соколов, відомий український математик і механік,- великий гуманіст і праведник. Світлій його пам'яті й присвячується ця статгя. Institute of Mathematics, NAS of Ukraine 1996-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5201 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 11 (1996); 1477-1483 Український математичний журнал; Том 48 № 11 (1996); 1477-1483 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5201/7096 https://umj.imath.kiev.ua/index.php/umj/article/view/5201/7097 Copyright (c) 1996 Gorbachuk M. L.; Yakymiv R. Ya. |
| spellingShingle | Gorbachuk, M. L. Yakymiv, R. Ya. Горбачук, М. Л. Якимів, Р. Я. Estimate of error of an approximated solution by the method of moments of an operator equation |
| title | Estimate of error of an approximated solution by the method of moments of an operator equation |
| title_alt | Оцінка похибки наближеного розв'язку операторного
рівняння методом моментів |
| title_full | Estimate of error of an approximated solution by the method of moments of an operator equation |
| title_fullStr | Estimate of error of an approximated solution by the method of moments of an operator equation |
| title_full_unstemmed | Estimate of error of an approximated solution by the method of moments of an operator equation |
| title_short | Estimate of error of an approximated solution by the method of moments of an operator equation |
| title_sort | estimate of error of an approximated solution by the method of moments of an operator equation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5201 |
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