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On the Convergence Theory of Preconditioned Subspace Iterations for Eigenvalue Problems
Author(s) -
Zhou Ming
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010269
Subject(s) - mathematics , subspace topology , eigenvalues and eigenvectors , convergence (economics) , krylov subspace , discretization , symbolic convergence theory , iterative method , mathematical analysis , mathematical optimization , computer science , physics , quantum mechanics , economics , economic growth , computer security , key (lock)
We consider preconditioned subspace iterations for the numerical solution of discretized elliptic eigenvalue problems. For these iterative solvers, the convergence theory is still an incomplete puzzle. We generalize some results from the classical convergence theory of inverse subspace iterations, as given by Parlett, and some recent results on the convergence of preconditioned vector iterations. To this end, we use a geometric cone representation and prove some new trigonometric inequalities for subspace angles and canonical angles. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)