Spectrum of a matrix

About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.

Rational and radical fixed point functions for the eigenvalue problem and polynomials

Abstract: The derivation and implementation of many algorithms in signal/image processing and control involve some form of polynomial root-finding and/or matrix eigendecomposition. In this paper, higher order fixed point functions in rational and/or radical forms are developed. This set of iterations can be considered as extensions of known methods such as the Newton, Lagurre and Halley methods and can be applied to compute all zeros of a polynomial as well as all eigenvalues of a complex matrix. One of the main features of the proposed algorithms is that they could have any predetermined rate of convergence regardless of the multiplicity of the zeros or eigenvalues. Additionally, eigenvalues and eigenvectors are computed using fast matrix inverse free algorithms which are based on the QR factorization.

Proposal of the Network Resonance Method for Estimating Eigenvalues of the Scaled Laplacian Matrix

Abstract: Eigenvalues of the Laplacian matrix play an important role in characterizing structural and dynamical properties of networks In the procedure for calculating eigenvalues of the Laplacian matrix, we need to get the Laplacian matrix that represents structures of the network Since the actual structure of networks and the strength of links are difficult to know, it is difficult to determine elements of the Laplacian matrix To solve this problem, our previous study proposed a concept of the network resonance method, which is for estimating eigenvalues of the scaled Laplacian matrix using resonance of oscillation dynamics on networks This method does not need a priori information about the network structure In this research, we investigate feasibility of the network resonance method, and show that the method can estimate eigenvalues of the scaled Laplacian matrix of the entire network through observations of oscillation dynamics even if observable nodes are restricted to a part of network

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Abstract: This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions on the geometrical (large width) and physical (large dielectric permittivity in modulus) properties of the strip that ensure the existence of positive eigenvalues are derived. Finally, we analyze the asymptotic behavior of the eigenvalues of A as the dielectric permittivity of the strip goes to -∞.

Asymptotic Behavior of the Steklov Eigenvalues For the p Laplace Operator

Abstract: In this paper we study the asymptotic behavior of the Steklov eigenvalues of the pLaplacian. We show the existence of lower and upper bounds of a Weyl-type expansion of the function N( ) which counts the number of eigenvalues less than or equal to , and we derive from them asymptotic bounds for the eigenvalues.

A forbidden set for embedded eigenvalues

Abstract: We study the problem of embedding eigenvalues to the spectrum of a Sturm-Liouville operator in the half axis when this spectrum is a perfect set. We prove the existence of an uncountable dense subset of the spectrum for which, by modifying the condition at the left or by locally perturbing the potential, it is not possible to add any eigenvalues.