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positive operators; complex Hilbert space; iteration subspace method; spectrum; eigenvalues; eigenvectors; Schmidt orthogonalization
The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators $A_n$ arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators $A_n$ is also considered.
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