Two different Lanczos-type methods for the linear response eigenvalue problem are analyzed. The first one is a natural extension of the classical Lanczos method for the symmetric eigenvalue problem while the second one was recently proposed by Tsiper specially for the linear response eigenvalue problem. Our analysis leads to bounds on errors for eigenvalue and eigenvector approximations by the ...

We prove that among all triangles of given diameter, the equilateral triangle minimizes the sum of the first n eigenvalues of the Neumann Laplacian, when n 3 . The result fails for n = 2 , because the second eigenvalue is known to be minimal for the degenerate acute isosceles triangle (rather than for the equilateral) while the first eigenvalue is 0 for every triangle. We show the third eigenva...

ABSTRACT. The so-called eigenvalues and eigenfunctions of the infinite Laplacian ∆∞ are defined through an asymptotic study of that of the usual p-Laplacian ∆p, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and re...