On the effective rank of finite dimentional approximations for the infinite dimentional linear measurement models

The problem of approximate calculation of effective rank of the linear model of the measuring is considered. The effective rank should be defined as maximum dimention of the orthogonal component of the signal, the component can be estimated with the rootmeansquare error, not higher than given value. It is indicated that the convergence of the sequence of finite dimentional models to the infinite dimentional models implies similar convergence of effective ranks. The rate of the convergence is found. The rezults obtained are illustrated by numerical examples.