The eigenvalue spectrum of covariance matrices is of central importance to a number of data analysis techniques. Usually the sample covariance matrix is constructed from a limited number of noisy samples. We describe a method of inferring the true eigenvalue spectrum from the sample spectrum. Results of Silverstein which characterise the eigenvalue spectrum of the noise covariance matrix and in...

One of the fundamental problems is to study the eigenvalue problem for the differential operator in geometric analysis. In this article, we introduce the recent developments of the eigenvalue problem for the Finsler Laplacian. M.S.C. 2010: 53C60; 35P30; 35J60.

In this paper the linear stability properties of the steady states of a no-slip lubrication equation are studied. The steady states are configurations of droplets and arise during the late-phase dewetting process under the influence of both destabilizing van der Waals and stabilizing Born intermolecular forces, which in turn give rise to the minimum thickness ε of the remaining film connecting ...

Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...

Motivated by problems involving diffusion through small gaps, we revisit twodimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O(jln ej), where e is the ratio of the size of the hole to the length-scale of the domain, and provide a simple and constructive approach for summing the inverse logarit...

We consider the quadrature method developed by Kravanja, Sakurai and Van Barel (BIT 39 (1999), no. 4, 646–682) for computing all the zeros of an analytic function that lie inside the unit circle. A new perturbation result for generalized eigenvalue problems allows us to obtain a detailed upper bound for the error between the zeros and their approximations. To the best of our knowledge, it is 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...

With the growing demands from disciplinary and interdisciplinary elds of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper, we examine the start-of-the-art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.

In this paper, the modified linearized Phillips-Heffron model is utilized to theoretically analyze asingle-machine infinite-bus (SMIB) installed with SSSC. Then, the results of this analysis are used forassessing the potential of an SSSC supplementary controller to improve the dynamic stability of apower system. This is carried out by measuring the electromechanical controllability through sing...

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...