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Keywords:
eigenvalues; eigenvectors; self-adjoint operators; spectrum
eigenvalues; eigenvectors; self-adjoint operators; spectrum
Summary:
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 $A$.
References:
[1] R. I. Andrushkiw: On the approximate solution of K-positive eigenvalue problems $T(u) - \lambda S(u) = 0$. J. Math. Anal. Appl. 50 (1975), 511 -527. DOI 10.1016/0022-247X(75)90007-4 | MR 0390817
[2] И. А. Биргер: Некоторые математические методы решения инженерных задач. Изд. Оборонгиз (Москва, 1956). Zbl 0995.90522
[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. MR 0129571
[4] J. Kolomý: On convergence of the iteration methods. Comment. Math. Univ. Carolinae 1 (1960), 18-24.
[5] J. Kolomý: On the solution of homogeneous functional equations in Hilbert space. Comment. Math. Univ. Carolinae 3 (1962), 36-47. MR 0149306
[6] J. Kolomý: Approximate determination of eigenvalues and eigenvectors of self-adjoint operators. Ann. Math. Pol. 38 (1980), 153 - 158. DOI 10.4064/ap-38-2-153-158 | MR 0599239
[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. MR 0540456
[8] M. А. Красносельский, другие: Приближенное решение операторных уравнений. Наука (Москва, 1969). Zbl 1149.62317
[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. MR 0149297 | Zbl 0192.23701
[10] I. Marek: Kellogg's iteration with minimizing parameters. Comment. Math. Univ. Carolinae 4 (1963), 53-64. MR 0172459
[11] Г. И. Марчук: Методы вычислительной математили. Изд. Наука (Новосибирск, 1973). Zbl 1170.01397
[12] W. V. Petryshyn: On the eigenvalue problem $T(u) - \lambda S(u) = 0$ 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. MR 0222697
[13] А. И. Плеснер: Спектральная теория линейных операторов. Изд. Наука (Москва, 1965). Zbl 1099.01519
[14] Wang Jin-Ru (Wang Chin-Ju): Gradient methods for finding eigenvalues and eigenvectors. Chinese Math. - Acta 5 (1964), 578-587. MR 0173358
[15] A. E. Taylor: Introduction in Functional Analysis. J. Wiley and Sons, Inc., New York, 1967.
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