TR-2008006: Additive Preconditioning, Eigenspaces, and the Inverse Iteration
نویسندگان
چکیده
We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic convergence, show experimentally that fast global convergence is preserved as well, and yield similar results for higher order inverse iteration, covering the cases of multiple and clustered eigenvalues.
منابع مشابه
TR-2007004: Additive Preconditioning, Eigenspaces, and the Inverse Iteration
Previously we have showed that the computation of vectors in and bases for the null space of a singular matrix can be accelerated based on additive preconditioning and aggregation. Now we incorporate these techniques into the inverse iteration for computing the eigenvectors and eigenspaces of a matrix, which are the null vectors and null spaces of the same matrix shifted by its eigenvalues. Acc...
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We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic conver...
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