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...
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Institute of Computer Science
2014-04-01
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Series: | Компьютерные исследования и моделирование |
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Online Access: | http://crm.ics.org.ru/uploads/crmissues/crm_2014_2/14201.pdf |
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doaj-31a1b7a99ba340e68a36cdc554a688dc2020-11-24T22:14:36ZrusInstitute 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 |
collection |
DOAJ |
language |
Russian |
format |
Article |
sources |
DOAJ |
author |
Boyuan Yuan A. I. Chulichkov |
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 |
author_facet |
Boyuan Yuan A. I. Chulichkov |
author_sort |
Boyuan Yuan |
title |
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_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_sort |
effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals |
publisher |
Institute of Computer Science |
series |
Компьютерные исследования и моделирование |
issn |
2076-7633 2077-6853 |
publishDate |
2014-04-01 |
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. |
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 |
work_keys_str_mv |
AT boyuanyuan effectiverankofaproblemoffunctionestimationbasedonmeasurementwithanerroroffinitenumberofitslinearfunctionals AT aichulichkov effectiverankofaproblemoffunctionestimationbasedonmeasurementwithanerroroffinitenumberofitslinearfunctionals |
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1725798114206416896 |