On determination of eigenvalues and eigenvectors of selfadjoint operators

Josef Kolomý

Aplikace matematiky (1981)

  • Volume: 26, Issue: 3, page 161-170
  • ISSN: 0862-7940

Abstract

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Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound λ 1 of the spectrum σ ( A ) of A is an isolated point of σ ( A ) ; (ii) λ 1 (not necessarily an isolated point of σ ( A ) with finite multiplicity) is an eigenvalue of A .

How to cite

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Kolomý, Josef. "On determination of eigenvalues and eigenvectors of selfadjoint operators." Aplikace matematiky 26.3 (1981): 161-170. <http://eudml.org/doc/15192>.

@article{Kolomý1981,
abstract = {Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound $\lambda _1$ of the spectrum $\sigma (A)$ of $A$ is an isolated point of $\sigma (A)$; (ii) $\lambda _1$ (not necessarily an isolated point of $\sigma (A)$ with finite multiplicity) is an eigenvalue of $A$.},
author = {Kolomý, Josef},
journal = {Aplikace matematiky},
keywords = {eigenvalues; eigenvectors; self-adjoint operators; spectrum; eigenvalues; eigenvectors; self-adjoint operators; spectrum},
language = {eng},
number = {3},
pages = {161-170},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On determination of eigenvalues and eigenvectors of selfadjoint operators},
url = {http://eudml.org/doc/15192},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Kolomý, Josef
TI - On determination of eigenvalues and eigenvectors of selfadjoint operators
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 3
SP - 161
EP - 170
AB - Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound $\lambda _1$ of the spectrum $\sigma (A)$ of $A$ is an isolated point of $\sigma (A)$; (ii) $\lambda _1$ (not necessarily an isolated point of $\sigma (A)$ with finite multiplicity) is an eigenvalue of $A$.
LA - eng
KW - eigenvalues; eigenvectors; self-adjoint operators; spectrum; eigenvalues; eigenvectors; self-adjoint operators; spectrum
UR - http://eudml.org/doc/15192
ER -

References

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  1. R. I. Andrushkiw, 10.1016/0022-247X(75)90007-4, J. Math. Anal. Appl. 50 (1975), 511 -527. (1975) MR0390817DOI10.1016/0022-247X(75)90007-4
  2. И. А. Биргер, Некоторые математические методы решения инженерных задач, Изд. Оборонгиз (Москва, 1956). (1956) Zbl0995.90522
  3. H. Bückner, An iterative method for solving nonlinear integral equations, Symp. on the numerical treatment of ordinary differential equations, integral and integro-differential equations, 613 - 643, Roma 1960, Birkhäuser Verlag, Basel- Stuttgart, 1960. (1960) MR0129571
  4. J. Kolomý, On convergence of the iteration methods, Comment. Math. Univ. Carolinae 1 (1960), 18-24. (1960) 
  5. J. Kolomý, On the solution of homogeneous functional equations in Hilbert space, Comment. Math. Univ. Carolinae 3 (1962), 36-47. (1962) MR0149306
  6. J. Kolomý, 10.4064/ap-38-2-153-158, Ann. Math. Pol. 38 (1980), 153 - 158. (1980) MR0599239DOI10.4064/ap-38-2-153-158
  7. J. Kolomý, Some methods for finding of eigenvalues and eigenvectors of linear and nonlinear operators, Abhandlungen der DAW, Abt. Math. Naturwiss. Tech., 1978, 6, 159-166, Akademie-Verlag, Berlin, 1978. (1978) MR0540456
  8. M. А. Красносельский, другие, Приближенное решение операторных уравнений, Наука (Москва, 1969). (1969) Zbl1149.62317
  9. I. Marek, Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iteration process, Czech. Math. Journal 12 (1962), 536-554. (1962) Zbl0192.23701MR0149297
  10. I. Marek, Kellogg's iteration with minimizing parameters, Comment. Math. Univ. Carolinae 4 (1963), 53-64. (1963) MR0172459
  11. Г. И. Марчук, Методы вычислительной математили, Изд. Наука (Новосибирск, 1973). (1973) Zbl1170.01397
  12. W. V. Petryshyn, On the eigenvalue problem T ( u ) - λ S ( u ) = 0 with unbounded and symmetric operators T and S, Phil. Trans. of the Royal Soc. of London, Ser. A. Math. and Phys. Sciences No 1130, Vol. 262 (1968), 413-458. (1968) MR0222697
  13. А. И. Плеснер, Спектральная теория линейных операторов, Изд. Наука (Москва, 1965). (1965) Zbl1099.01519
  14. Wang Jin-Ru (Wang Chin-Ju), Gradient methods for finding eigenvalues and eigenvectors, Chinese Math. - Acta 5 (1964), 578-587. (1964) MR0173358
  15. A. E. Taylor, Introduction in Functional Analysis, J. Wiley and Sons, Inc., New York, 1967. (1967) 

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