in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof of the conclusion stating that if 1 is an eigenvalue of the Smatrix, then k2 is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet pro...

The trust-region subproblem of minimizing a quadratic function subject to a norm constraint arises in the context of trust-region methods in optimization and in the regularization of discrete forms of ill-posed problems, including non-negative regularization by means of interior-point methods. A class of efficient methods and software for solving large-scale trust-region subproblems is based on...

In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix whose samples are in the frequency domain. Soft combining of the eigenvalues at the fusion center is the main novelty. Thi...

We consider elliptic operators in divergence form L = div (Φ · grad ) either on a closed Riemannian manifold or in a domain with compact closure and piecewise smooth boundary M where Φ : M → End(TM) is a positive definite symmetric smooth section of the bundle of all endomorphisms of TM . We show that the first nonzero L-eigenvalues in the closed or Dirichlet eigenvalue problems can be bounded ...

The main aim of this paper is to construct quantum extension of the discrete Sturm–Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. ...

The problem of eigenvalue placement via state observer for generalized linear time invariant systems is considered. The main contribute is to whow that even if the well-known Luenberger eigenvalue separation theorem may be easily extended to the generalized case, the solvability of the resulting compensator is not in general assured. It is shown that regularity may be reached by a suitable choi...

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 article is concerned with recent developments of adaptive wavelet solvers for elliptic eigenvalue problems. We describe the underlying abstract iteration scheme of the preconditioned perturbed iteration. We apply the iteration to a simple model problem in order to identify the main ideas which a numerical realization of the abstract scheme is based upon. This indicates how these concepts c...

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.