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Newton's Method for a Generalized Inverse Eigenvalue Problem
Author(s) -
Dai Hua,
Lancaster Peter
Publication year - 1997
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199701/02)4:1<1::aid-nla95>3.0.co;2-d
Subject(s) - mathematics , eigenvalues and eigenvectors , newton's method , inverse , inverse iteration , divide and conquer eigenvalue algorithm , calculus (dental) , mathematical analysis , geometry , nonlinear system , physics , quantum mechanics , medicine , dentistry
A kind of generalized inverse eigenvalue problem is proposed which includes the additive, multiplicative and classical inverse eigenvalue problems as special cases. Newton's method is applied, and a local convergence analysis is given for both the distinct and the multiple eigenvalue cases. When the multiple eigenvalues are present we show how to state the problem so that it is not over‐determined, and discuss a Newton‐method for the modified problem. We also prove that the modified method retains quadratic convergence, and present some numerical experiments to illustrate our results. © 1997 by John Wiley & Sons, Ltd.