Summary
In recent years, a group of inverse iteration type algorithms have been developed for solving nonlinear elliptic eigenvalue problems in plasma physics [4]. Although these algorithms have been very successful in practice, no satisfactory theoretical justification of convergence has been available. The present paper fills this gap and proves for a large class of such problems and a simple version of such algorithms that linear convergence to a local maximum of a certain potential is obtained.
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This work was supported by the Deutsche Forschungsgemeinschaft, SFB 72 an der Universität Bonn
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Georg, K. On the convergence of an inverse iteration method for nonlinear elliptic eigenvalue problems. Numer. Math. 32, 69–74 (1979). https://doi.org/10.1007/BF01397650
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DOI: https://doi.org/10.1007/BF01397650