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Methods of simultaneous calculation of some eigenvectors. (O metodakh odnovremennogo vychisleniya neskol’kikh sobstvennykh vektorov.) (Russian) Zbl 0706.65035
Preprint, Institut Atomnoj Ehnergii Im. I. V. Kurchatova, IAEh-3724/16. Moskva: Institut Atomnoj Ehnergii Im. I. V. Kurchatova. 20 p. R. 0.20 (1983).
Summary: Numerical methods for the simultaneous determination of several lower eigenvalues and eigensubspaces correspond to those ones for the generalized eigenvalue problem with symmetric and positive definite matrices.
Estimates of accuracy of approximations to eigenvalues by the Ritz method, implying also estimates of accuracy of approximations to eigensubspaces in terms of apertures of subspaces in different metrics, are derived from simple relations for the apertures.
Estimates of the convergence rate are obtained for the methods of simultaneous iterations. On their basis the notion of optimality is defined. It is shown that estimates of the convergence rate for the optimal method of simultaneous iterations are unimprovable.
Estimates of the convergence rate for the block Lanczos method are presented which improve the known ones.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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