Min-plus Methods in Eigenvalue Perturbation Theory and Generalised Lidskĭi-višik-ljusternik Theorem
نویسنده
چکیده
We extend the perturbation theory of Vǐsik, Ljusternik and Lidskĭı for eigenvalues of matrices, using methods of min-plus algebra. We show that the asymptotics of the eigenvalues of a perturbed matrix is governed by certain discrete optimisation problems, from which we derive new perturbation formulæ, extending the classical ones and solving cases which where singular in previous approaches. Our results include general weak majorisation inequalities, relating leading exponents of eigenvalues of perturbed matrices and min-plus analogues of eigenvalues.
منابع مشابه
On the Variational Eigenvalues Which Are Not of Ljusternik-Schnirelmann Type
and Applied Analysis 3 Every λk is a critical level of F subject to S, and it is achieved at some uk ∈ S, that is, F|S ′ uk 0 7 cf. 4, 5 . It follows that λk is an eigenvalue of 1 and uk is the corresponding eigenvector. In general, the sequence {λk}k 1 given by 6 does not exhaust the set of all critical levels of F|S, and thus it might not be the set of all eigenvalues of 1 . An eigenvalue of ...
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