Geodesic
The accuracy estimation of the numerical solution of the spectral problem with the operator depending on the eigenvalue
Matematičeskoe modelirovanie, Tome 15 (2003) no. 1, pp. 87-100.

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The spectral problems with the eigenvalue-depending operator are usually appeared when the relative variants of the Schroedinger equation in the impulse space are considered. The eigenvalues and eigenfunctions calculation error caused by the numerical solving of such equations is the sum of the error entering the approximation of a continuous equation by the discret equations system with help the Bubnov–Galerkine method and the iterative method. It is shown that the iterative method error is one-two order smaller than for discretisation problem. Hense, the eigenvalues and eigenfunctions calculation accuracy of the spectral problem with the eigenvalue-depending operator is not worse then the linear spectral problem solution accuracy. 
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E. P. Zhidkov; N. B. Skachkov; T. M. Solov'eva. The accuracy estimation of the numerical solution of the spectral problem with the operator depending on the eigenvalue. Matematičeskoe modelirovanie, Tome 15 (2003) no. 1, pp. 87-100. http://geodesic.mathdoc.fr/item/MM_2003_15_1_a8/

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