Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals
The problem of restoration of an element f of Euclidean functional space L2(X) based on the results of measurements of a finite set of its linear functionals, distorted by (random) error is solved. A priori data aren't assumed. Family of linear subspaces of the maximum (effective) dimension fo...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
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Institute of Computer Science
2014-04-01
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| Series: | Компьютерные исследования и моделирование |
| Subjects: | |
| Online Access: | http://crm.ics.org.ru/uploads/crmissues/crm_2014_2/14201.pdf |
| _version_ | 1818616036380901376 |
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| author | Boyuan Yuan A. I. Chulichkov |
| author_facet | Boyuan Yuan A. I. Chulichkov |
| author_sort | Boyuan Yuan |
| collection | DOAJ |
| description | The problem of restoration of an element f of Euclidean functional space L2(X) based on the results of measurements of a finite set of its linear functionals, distorted by (random) error is solved. A priori data aren't assumed. Family of linear subspaces of the maximum (effective) dimension for which the projections of element f to them allow estimates with a given accuracy, is received. The effective rank () of the estimation problem is defined as the function equal to the maximum dimension of an orthogonal component Pf of the element f which can be estimated with a error, which is not surpassed the value . The example of restoration of a spectrum of radiation based on a finite set of experimental data is given. |
| first_indexed | 2024-12-16T16:43:25Z |
| format | Article |
| id | doaj.art-31a1b7a99ba340e68a36cdc554a688dc |
| institution | Directory Open Access Journal |
| issn | 2076-7633 2077-6853 |
| language | Russian |
| last_indexed | 2024-12-16T16:43:25Z |
| publishDate | 2014-04-01 |
| publisher | Institute of Computer Science |
| record_format | Article |
| series | Компьютерные исследования и моделирование |
| spelling | doaj.art-31a1b7a99ba340e68a36cdc554a688dc2022-12-21T22:24:14ZrusInstitute of Computer ScienceКомпьютерные исследования и моделирование2076-76332077-68532014-04-016218920210.20537/2076-7633-2014-6-2-189-2022137Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionalsBoyuan YuanA. I. ChulichkovThe problem of restoration of an element f of Euclidean functional space L2(X) based on the results of measurements of a finite set of its linear functionals, distorted by (random) error is solved. A priori data aren't assumed. Family of linear subspaces of the maximum (effective) dimension for which the projections of element f to them allow estimates with a given accuracy, is received. The effective rank () of the estimation problem is defined as the function equal to the maximum dimension of an orthogonal component Pf of the element f which can be estimated with a error, which is not surpassed the value . The example of restoration of a spectrum of radiation based on a finite set of experimental data is given.http://crm.ics.org.ru/uploads/crmissues/crm_2014_2/14201.pdfmathematical model of measurementmeasurement reductionspectrometryoptimum decisionssingular decompositioneffective rank |
| spellingShingle | Boyuan Yuan A. I. Chulichkov Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals Компьютерные исследования и моделирование mathematical model of measurement measurement reduction spectrometry optimum decisions singular decomposition effective rank |
| title | Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
| title_full | Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
| title_fullStr | Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
| title_full_unstemmed | Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
| title_short | Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
| title_sort | effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
| topic | mathematical model of measurement measurement reduction spectrometry optimum decisions singular decomposition effective rank |
| url | http://crm.ics.org.ru/uploads/crmissues/crm_2014_2/14201.pdf |
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