It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

As defined, the e.d.f. is right continuous and possibly atomic i.e. with step discontinuities at discrete points. In practical terms, the derivative of (1), referred to as the (eigenvalue) level density, is simply the appropriately normalized histogram of the eigenvalues of AN . The MATLAB code histn we distributed earlier approximates this density. A surprising result in infinite RMT is that f...

For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

Contour integration schemes are a valuable tool for the solution of difficult interior eigenvalue problems. However, many large linear systems with multiple right hand sides may prove prohibitive computational expense. The number sides, and thus, cost be reduced if projected subspace is created using moments. In this work, we explore heuristics choice application moments respect to various othe...

In this article we characterize the L mathvariant="normal">∞ <mml:annotation encoding="application/...

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spa...