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ON THE CONVERGENCE OF ZERO‐FINDING EIGENSOLUTION ALGORITHMS FOR SOLVING NON‐LINEAR EIGENVALUE PROBLEMS
Author(s) -
ABDELAZIZ MOHAMMEDI R.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970615)40:11<2037::aid-nme157>3.0.co;2-x
Subject(s) - eigenvalues and eigenvectors , convergence (economics) , zero (linguistics) , divide and conquer eigenvalue algorithm , mathematics , solver , rate of convergence , focus (optics) , algorithm , mathematical optimization , computer science , key (lock) , linguistics , philosophy , physics , quantum mechanics , economics , economic growth , computer security , optics
This paper presents a convergence theory for non‐linear eigenvalue methods. The basic idea of these methods, which have been described by the author in an earlier paper, is to apply an eigen‐solver in conjunction with a zero‐finding technique for solving the non‐linear eigenvalue problems. The main focus of the paper is to study the rate of convergence of these techniques when they are applied to solve the dependent symmetric eigenproblems. The results are proved to the zero‐finders which are based on rational approximation and they are used to update the eigenvalue γ. © 1997 by John Wiley & Sons, Ltd.