NDLI: Dynamical Systems and Non-Hermitian Iterative Eigensolvers

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Embree, Mark Lehoucq, Richard B.
Copyright Year	2009
Abstract	Simple preconditioned iterations can provide an efficient alternative to more elaborate eigenvalue algorithms. We observe that these simple methods can be viewed as forward Euler discretizations of well-known autonomous differential equations that enjoy appealing geometric properties. This connection facilitates novel results describing convergence of a class of preconditioned eigensolvers to the leftmost eigenvalue, provides insight into the role of orthogonality and biorthogonality, and suggests the development of new methods and analyses based on more sophisticated discretizations. These results also highlight the effect of preconditioning on the convergence and stability of the continuous-time system and its discretization.
Starting Page	1445
Ending Page	1473
Page Count	29
File Format	PDF
ISSN	00361429
DOI	10.1137/07070187X
e-ISSN	10957170
Issue Number	2
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-03-13
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods Eigenvalues, singular values, and eigenvectors dynamical systems eigenvalues Eigenvalues, eigenvectors geometric invariants Vector fields, flows, ordinary differential equations inverse iteration preconditioned eigensolvers
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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