Additive preconditioning, eigenspaces, and the inverse iteration |
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Authors: | Victor Y Pan Xiaodong Yan |
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Institution: | a Department of Mathematics and Computer Science, Lehman College of the City University of New York, Bronx, NY 10468, USA b The City University of New York, New York, NY 10036, USA |
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Abstract: | 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. |
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Keywords: | Additive preconditioning Eigenspaces Inverse iteration |
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