In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here with an approach based on the diierential formulation of perturbation theory where the high order perturbation c...

As applications on massive data sets are emerging with an increasing frequency, we are facing the problem of analyzing the data as soon as they are produced. This is true in many fields of science and engineering: in high energy physics, experiments have been done to transfer data at a sustained rate of 150 gigabits per second. In Y2007, that speed will enable the delivery to users of data cont...

In this paper, we examine the maximum eigenvalue function of an even order real symmetric tensor. By using the variational analysis techniques, we first show that the maximum eigenvalue function is a continuous and convex function on the symmetric tensor space. In particular, we obtain the convex subdifferential formula for the maximum eigenvalue function. Next, for an mth-order n-dimensional s...

We report on a parallel implementation of the Jacobi–Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem

We characterize the possible lists of ordered multiplicities among matrices whose graph is a generalized star (a tree in which at most one vertex has degree greater than 2) or a double generalized star. Here, the inverse eigenvalue problem for symmetric matrices whose graph is a generalized star is settled. The answer is consistent with a conjecture that determination of the possible ordered mu...

Recent progress in signal processing and estimation has generated considerable interest in the problem of computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix. Several algorithms have been proposed in the literature. Many of them compute the smallest eigenvalue in an iterative fashion, relying on the Levinson–Durbin solution of sequences of Yule–Walker systems. Exp...