Inertia‐based spectrum slicing for symmetric quadratic eigenvalue problems
Summary In the quadratic eigenvalue problem (QEP) with all coefficient matrices symmetric, there can be complex eigenvalues. However, some applications need to compute real eigenvalues only. We propose a Lanczos‐based method for computing all real eigenvalues contained in a given interval of large‐s...
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Published in | Numerical linear algebra with applications Vol. 27; no. 4 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Oxford
Wiley Subscription Services, Inc
01.08.2020
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Subjects | |
Online Access | Get full text |
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Summary: | Summary
In the quadratic eigenvalue problem (QEP) with all coefficient matrices symmetric, there can be complex eigenvalues. However, some applications need to compute real eigenvalues only. We propose a Lanczos‐based method for computing all real eigenvalues contained in a given interval of large‐scale symmetric QEPs. The method uses matrix inertias of the quadratic polynomial evaluated at different shift values. In this way, for hyperbolic problems, it is possible to make sure that all eigenvalues in the interval have been computed. We also discuss the general nonhyperbolic case. Our implementation is memory‐efficient by representing the computed pseudo‐Lanczos basis in a compact tensor product representation. We show results of computational experiments with a parallel implementation in the SLEPc library. |
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Bibliography: | Funding information Agencia Estatal de Investigación, TIN2016‐75985‐P |
ISSN: | 1070-5325 1099-1506 |
DOI: | 10.1002/nla.2293 |