A simple extrapolation method for clustered eigenvalues
| Autor: | Nilima Nigam, Sara Pollock |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Numerical analysis Extrapolation 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences 010101 applied mathematics Power iteration Simple (abstract algebra) Convergence (routing) FOS: Mathematics Applied mathematics Spectral gap Mathematics - Numerical Analysis 0101 mathematics Linear combination Eigenvalues and eigenvectors 65B05 65F15 Mathematics |
| DOI: | 10.48550/arxiv.2006.10164 |
| Popis: | This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small spectral gap. The introduced method is a one-step extrapolation technique that uses a linear combination of current and previous update steps to form a better approximation of the dominant eigenvector. The provided analysis shows the method converges exponentially with respect to the ratio between the two largest eigenvalues, which is also approximated during the process. An augmented technique is also introduced, and is shown to stabilize the early stages of the iteration. Numerical examples are provided to illustrate the theory and demonstrate the methods. Comment: 20 pages, 7 figures, 4 tables. Updated version includes additional numerical tests, including nonsymmetric systems |
| Databáze: | OpenAIRE |
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