Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals

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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 to them allow estimates with a given accuracy, is received. The effective rank ρ(δ) 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 δ. The example of restoration of a spectrum of radiation based on a finite set of experimental data is given.

Keywords: mathematical model of measurement, measurement reduction, spectrometry, optimum decisions, singular decomposition, effective rank
Citation in English: Chulichkov A.I., Yuan B. Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals // Computer Research and Modeling, 2014, vol. 6, no. 2, pp. 189-202

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