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Newton's Method for a Generalized Inverse Eigenvalue Problem

✍ Scribed by Hua Dai; Peter Lancaster

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 151 KB
Volume: 4
Category: Article
ISSN: 1070-5325
DOI: 10.1002/(sici)1099-1506(199701/02)4:1<1::aid-nla95>3.0.co;2-d

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✦ Synopsis

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.

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