A Geometric Theory for Preconditioned Inverse Iteration Ii: Convergence Estimates
نویسنده
چکیده
The topic of this paper is a convergence analysis of preconditioned inverse iteration (PINVIT). A sharp estimate for the eigenvalue approximations is derived; the eigenvector approximations are controlled by an upper bound for the residual vector. The analysis is mainly based on extremal properties of various quantities which define the geometry of PINVIT.
منابع مشابه
A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
In two previous papers by Neymeyr: A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient, LAA 322: (1-3), 61-85, 2001, and A geometric theory for preconditioned inverse iteration II: Convergence estimates, LAA 322: (1-3), 87-104, 2001, a sharp, but cumbersome, convergence rate estimate was proved for a simple preconditioned eigensolver, which computes the s...
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