Spectral approximation of positive operators by iteration subspace method

Andrzej Pokrzywa

Aplikace matematiky (1984)

  • Volume: 29, Issue: 2, page 104-113
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Pokrzywa, Andrzej. "Spectral approximation of positive operators by iteration subspace method." Aplikace matematiky 29.2 (1984): 104-113. <http://eudml.org/doc/15338>.

@article{Pokrzywa1984,
abstract = {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.},
author = {Pokrzywa, Andrzej},
journal = {Aplikace matematiky},
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},
language = {eng},
number = {2},
pages = {104-113},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral approximation of positive operators by iteration subspace method},
url = {http://eudml.org/doc/15338},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Pokrzywa, Andrzej
TI - Spectral approximation of positive operators by iteration subspace method
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 2
SP - 104
EP - 113
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/15338
ER -

References

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  1. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin- Heidelberg- New York, 1966. (1966) Zbl0148.12601MR0203473
  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. (1980) MR0618027
  3. J. Kolomý, On determination of eigenvalues and eigenvectors of self-adjoint operators, Apl. Mat. 26 (1981), pp. 161-170. (1981) MR0615603
  4. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Inc., Englewood Cliffs, 1980. (1980) Zbl0431.65017MR0570116
  5. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. (1965) Zbl0258.65037MR0184422

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