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Keywords:
positive operators; complex Hilbert space; iteration subspace method; spectrum; eigenvalues; eigenvectors; Schmidt orthogonalization
positive operators; complex Hilbert space; iteration subspace method; spectrum; eigenvalues; eigenvectors; Schmidt orthogonalization
Summary:
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.
References:
[1] T. Kato: Perturbation Theory for Linear Operators. Springer-Verlag, Berlin- Heidelberg- New York, 1966. MR 0203473 | Zbl 0148.12601
[2] J. Kolomý: Determination of eigenvalues and eigenvectors of self-adjoint operators. Mathematica - Revue d'analyse numerique et de theorie de l'approximation. 22 (45), No 1, 1980, pp. 53-58. MR 0618027
[3] J. Kolomý: On determination of eigenvalues and eigenvectors of self-adjoint operators. Apl. Mat. 26 (1981), pp. 161-170. MR 0615603
[4] B. N. Parlett: The Symmetric Eigenvalue Problem. Prentice-Hall, Inc., Englewood Cliffs, 1980. MR 0570116 | Zbl 0431.65017
[5] J. H. Wilkinson: The Algebraic Eigenvalue Problem. Clarendon Press, Oxford, 1965. MR 0184422 | Zbl 0258.65037
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