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An approximative solution of the generalized eigenvalue problem. (English) Zbl 0781.47029
In this note an algorithm and its convergence to the solution of the equation \[ Ax=\lambda Bx \tag{1} \] is shown, where \(x\in X\), \(X\) is a Hilbert space and \(A\) and \(B\) are linear operators from \(X\) onto \(X\). There are used some terms of the theory of the spectral representation of a normal operator.
47A75 Eigenvalue problems for linear operators
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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[1] Dunford N., Schwartz J.T.: Linejnye operatory I (II). Mir, Moskva 1962 (1966).
[2] Kojecký T.: Some results about convergence of Kellogg’s iterations in eigenvalue problems. Czech. Math. J.
[3] Kojecký T.: Iterative solution of eigenvalue problems for normal operator. Apl. mat. · Zbl 0708.65055
[4] Kolomý J.: On the Kellogg method and its variants for finding of eigenvalues and eigenfunctions of linear self-adjoint operators. ZAA Bd. 2(4) 1983, 291-297. · Zbl 0532.65042
[5] Marek I.: Iterations of linear bounded operators in non-self-adjoint eigenvalue problems and Kellogg’s iteration process. Czech. Math. J. 12 (1962), 536-554. · Zbl 0192.23701
[6] Nashed M.Z.: General inverses, normal solvability and iteration for singular operator equations, nonlinear functional analysis and applications. Academia Press, New York, 1971, 311-359.
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