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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Main Authors: Boyuan Yuan, A. I. Chulichkov
Format: Article
Language:Russian
Published: Institute of Computer Science 2014-04-01
Series:Компьютерные исследования и моделирование
Subjects:
Online Access:http://crm.ics.org.ru/uploads/crmissues/crm_2014_2/14201.pdf
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spelling 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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