Presented are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomp...

For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take different values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers. Our main result is that a multiple eigenvalue generally has multiple cond...

The class of connected 3-colored digraphs containing exactly one nonsingular cycle is considered in this article. The main objective is to study the smallest Laplacian eigenvalue and the corresponding eigenvectors of such graphs. It is shown that the smallest Laplacian eigenvalue of such a graph can be realized as the algebraic connectivity (second smallest Laplacian eigenvalue) of a suitable u...

In this paper, we consider the eigenvalue problems for fourth order integral boundary value problems on time scales for an increasing homeomorphism and homomorphism with sign changing nonlinearities. By using a fixed point index theorem, we give the existence of eigenvalue intervals in which there exist one symmetric positive solution to the problem. An example is also given to demonstrate the ...

The main ideas of path following by predictor-corrector and piecewise-linear methods, and their application in the direction of homotopy methods and non-linear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed...

It was conjectured by Doron and Smilansky (DS) in 1992 that k2 > 0 is a Dirichlet eigenvalue of the Laplacian in a bounded domain D if and only if the corresponding S-matrix for the scattering problem by the obstacle D has an eigenvalue 1. The main results of this paper are: 1) a proof that the DS conjecture is incorrect, 2) a proof that a necessary condition for 1 to be an eigenvalue of the S-...

This paper is concerned with the existence, nonexistence, uniqueness, and multiplicity of positive solutions for a class of eigenvalue problems of nonlinear fractional differential equations with a nonlinear integral term and a disturbance parameter in the boundary conditions. By using fixed point index theory we give the critical curve of eigenvalue λ and disturbance parameterμ that divides th...

A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

The aim of the book is to provide an analysis of the boundary element method for the numerical solution of Laplacian eigenvalue problems. The representation of Laplacian eigenvalue problems in the form of boundary integral equations leads to nonlinear eigenvalue problems for related boundary integral operators. The solution of boundary element discretizations of such eigenvalue problems require...

Abstract. The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a large class of...