Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals
| Autor: | Boyuan Yuan, A. I. Chulichkov |
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| Jazyk: | ruština |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Компьютерные исследования и моделирование, Vol 6, Iss 2, Pp 189-202 (2014) |
| Druh dokumentu: | article |
| ISSN: | 2076-7633 2077-6853 |
| DOI: | 10.20537/2076-7633-2014-6-2-189-202 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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