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Eigenvalue approximation. (English) Zbl 0583.65035
Computational mathematics, Banach Cent. Publ. 13, 559-573 (1984).
[For the entire collection see Zbl 0556.00012.]
The selfadjoint eigenvalue problem \[ find\quad \mu \in {\mathbb{R}}\quad and\quad 0\neq u\in V\quad such\quad that\quad b(u,v)=\mu \cdot (u,v)\quad \forall v\in V \] is solved in a Hilbert space V. This problem is approximated by a family of eigenvalue problems on finite-dimensional spaces. Sufficient conditions for convergent approximations are given. The eigenvalues are found using Rayleigh quotients. The convergence of the method is proved and error estimates as well as some examples are given.
Reviewer: L.Boubelíková

MSC:
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
47A10 Spectrum, resolvent
34L99 Ordinary differential operators