In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that permit the use of fast solvers. The main innovation is that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional e...

We calculate the main asymptotic terms for eigenvalues, both simple and multiple, and eigenfunctions of the Neumann Laplacian in a three-dimensional domain Ω(h) perturbed by a small (with diameter O(h)) Lipschitz cavern ωh in a smooth boundary ∂Ω = ∂Ω(0). The case of the hole ωh inside the domain but very close to the boundary ∂Ω is under consideration as well. It is proven that the main correc...

Recently, a new blind spectrum sensing technique based on signal space dimension estimation was developed for sensing the spectrum holes in the primary user’s bands. The mean idea of this technique is that the number of significant eigenvalues of the covariance matrix of the received signal is directly related to the presence/absence of data in the signal. In this paper, we study the collaborat...

For periodic Toda chains with a large number N of particles we consider states which are N−2-close to the equilibrium and constructed by discretizing arbitrary given C2−functions with mesh size N−1. Our aim is to describe the spectrum of the Jacobi matrices LN appearing in the Lax pair formulation of the dynamics of these states as N → ∞. To this end we construct two Hill operators H± – such op...

| In this paper dynamic exponent-based electronics is introduced as a good candidate for overcoming some of the limitations of classic linear-based electronics. However, the use of the exponential relation as a primitive for the synthesis of electronic circuits implies that we have to deal with analysis and synthesis of dynamic nonlinear circuits. The linear time-varying approximation appears t...

A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius R increases, eigenvalue spectra converge to the absolute spectrum predicted by Sandstede and Scheel. The convergence rate is consistent with 1/R, except possibly near the edge of the spectrum. Eigenfunctions computed on large disks are compared with predicte...

In this paper we present an iterative method, inspired by the inverse iteration with shift technique of finite linear algebra, designed to find the eigenvalues and eigenfunctions of the Laplacian with homogeneous Dirichlet boundary condition for arbitrary bounded domains X R . This method, which has a direct functional analysis approach, does not approximate the eigenvalues of the Laplacian as ...

Applications such as the modal analysis of structures and acoustic cavities require a number of eigenvalues and eigenvectors of large scale Hermitian eigenvalue problems. The most popular method is probably the spectral transformation Lanczos method. An important disadvantage of this method is that a change of pole requires a complete restart. In this paper, we investigate the use of the ration...

The elastic moduli of vortex crystals in anisotropic superconductors are frequently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigenvalues ~normal modes! of the vortex lattice for general values of the magnetic field strength, going beyond the elastic continuum regime. The detailed behavior of these wave-vector-d...

April 28, 2010 Type Package Title A Parallel Analysis With Polychoric Correlation Matrices Version 1.1 Date 2010-04-07 Author Fabio Presaghi & Marta Desimoni Maintainer Fabio Presaghi Description The Function performs a parallel analysis using simulated polychoric correlation matrices. The nth-percentile of the eigenvalues distribution obtained from both the randoml...