We reconsider MMSE-based time-domain equalizer (TEQ), bitrate maximizing TEQ and per-tone equalizer design for DMT transmission. It is shown that they can all be formulated either as a constrained linear or a separable nonlinear least-squares problem. These least-squares formulations are then turned into generalized eigenvalue problems that allow to establish a remarkably close relationship bet...

A graph’s spread is defined as the difference between the largest eigenvalue and the least eigenvalue of the graph’s adjacency matrix. Characterizing a graph with maximal spread is still a difficult problem. If we restrict the discussion to some classes of connected graphs of a prescribed order and size, it simplifies the problem and it may allow us to solve it. Here, we discuss some results on...

Abstract. Much of the work of Golub and his collaborators uses techniques of linear algebra to deal with problems in analysis, or employs tools from analysis to solve problems arising in linear algebra. Instances are described of such interdisciplinary work, taken from quadrature theory, orthogonal polynomials, and least squares problems on the one hand, and error analysis for linear algebraic ...

Namyong Kim 155 In this paper, we introduce an escalator (ESC) algorithm based on the least squares (LS) criterion. The proposed algorithm is relatively insensitive to the eigenvalue spread ratio (ESR) of an input signal and has a faster convergence speed than the conventional ESC algorithms. This algorithm exploits the fast adaptation ability of least squares methods and the orthogonalization ...

We study inexact subspace iteration for solving generalized non-Hermitian eigenvalue problems with spectral transformation, with focus on a few strategies that help accelerate preconditioned iterative solution of the linear systems of equations arising in this context. We provide new insights into a special type of preconditioner with “tuning” that has been studied for this algorithm applied to...

We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. graphs on N vertices where every edge is chosen independently and with probability p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption pN N, we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we pro...