Using QR-like decomposition with column pivoting and least squares techniques, we propose a new and ecient algorithm for solving symmetric generalized inverse eigenvalue problems, and give its locally quadratic convergence analysis. We also present some numerical experiments which illustrate the behaviour of our algorithm. Ó 1999 Elsevier Science Inc. All rights reserved. AMS classi®cation: 65...

Abstract: The basic least squares method for identifying linear systems has been extensively studied. Conditions for convergence involve issues about noise assumptions and behavior of the sample covariance matrix of the regressors. Lai and Wei proved in 1982 convergence for essentially minimal conditions on the regression matrix: All eigenvalues must tend to infinity, and the logarithm of the l...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

The paper is concerned with a sequence of constants which appear in several problems. These problems include the minimal eigenvalue of certain positive definite Toeplitz matrices, the minimal eigenvalue of some higher-order ordinary differential operators, the norm of the Green kernels of these operators, the best constant in a Wirtinger-Sobolev inequality, and the conditioning of a special lea...

This paper presents a method for computing partial spectra of Hermitian matrices, based on a subspace iteration method combined with rational filtering. While the general approach is the same as that of the FEAST package, the emphasis of this paper is on the selection of the filter. Specifically, the goal is to show the appeal of a least-squares viewpoint for designing filters. In particular, t...

We consider the problem of how the least eigenvalue of a SturmLiouville problem changes as the coefficients are varied. For a certain class of such problems, it is proved that the least eigenvalue can be maximized by placing constraints on the coefficients. Applications are made to various types of column problems. As a preliminary, we develop the spectral theory for a one term operator which h...

Let G be a finite graph with μ as an eigenvalue of multiplicity k. A star set for μ is a set X of k vertices in G such that μ is not an eigenvalue of G−X. We investigate independent star sets of largest possible size in a variety of situations. We note connections with symmetric designs, codes, strongly regular graphs, and graphs with least eigenvalue −2. AMS Classification: 05C50

Let U(n, k) be the set of non-bipartite unicyclic graphs with n vertices and k pendant vertices, where n ≥ 4. In this paper, the unique graph with the minimal least eigenvalue of the signless Laplacian among all graphs in U(n, k) is determined. Furthermore, it is proved that the minimal least eigenvalue of the signless Laplacian is an increasing function in k. Let Un denote the set of non-bipar...