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Eigenvalue perturbation and generalized Krylov subspace method

โœ Scribed by T. Zhang; G.H. Golub; K.H. Law

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
909 KB
Volume
27
Category
Article
ISSN
0168-9274

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โœฆ Synopsis

In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here an approach based on the differential formulation of perturbation theory where the high order perturbation can be naturally obtained. The high order perturbation can be interpreted as a generalized Krylov subspace approximation and its convergence rate can be analyzed accordingly. This approach provides a simple and stable method to compute a few eigenvalues of a slightly modified system.

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Deflated block Krylov subspace methods for large scale eigenvalue problems
โœ Qiang Niu; Linzhang Lu ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 530 KB

We discuss a class of deflated block Krylov subspace methods for solving large scale matrix eigenvalue problems. The efficiency of an Arnoldi-type method is examined in computing partial or closely clustered eigenvalues of large matrices. As an improvement, we also propose a refined variant of the A