A new Neumann-Neumann type domain decomposition algorithm for the solution of contact problems of elasticity and similar problems is described. The discretized variational inequality that models the equilibrium of a system of elastic bodies in contact is first turned by duality to a strictly convex quadratic programming problem with either box constraints or box and equality constraints. This s...

In this paper we consider Lur'e systems where a linear dynamical system is feedback interconnected to a multilayer perceptron nonlinearity, corresponding to recurrent neural networks with two hidden layers. For this class of nonlinear systems, we present suu-cient conditions for global asymptotic stability based on quadratic and Lur'e-Postnikov Lyapunov functions. Suucient conditions for dissip...

Given a simple, undirected graph G, Budinich [Discrete Applied Mathematics, 127 (2003), 535 – 543] proposed a lower bound on the clique number of G by combining the quadratic programming formulation of the clique number due to Motzkin and Straus (1965) with the spectral decomposition of the adjacency matrix of G. This lower bound improves the previously known spectral lower bounds on the clique...

A connection between the convolutive nonnegative matrix factorization (NMF) and the conventional NMF has been established. As a results, we can convey arbitrary alternating update rules for NMF to update rules for CNMF. In order to illustrate the novel derivation method, a new ALS algorithm for CNMF is proposed based on solving nonnegative quadratic programming problems. The experiment will con...

We study prime algebras of quadratic growth. Our first result is that if A is a prime monomial algebra of quadratic growth then A has finitely many prime ideals P such that A/P has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the non...

<abstract><p>Consider the problem of finding maximal nonpositive solvent $ \varPhi quadratic matrix equation (QME) X^2 + BX C = 0 with B being a nonsingular M $-matrix and an such that B^{-1}C\ge $. Such QME arises from overdamped vibrating system. Recently, under condition - I is $-matrix, Yu et al. (<italic>Appl. Math. Comput.</italic>, 218 (2011): 3303–3310) proved \r...

An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to original ones in compact matrix format. Keywords—Quadratic forms, characteristic function, multichannel communication systems.

Based on a differential inclusion approach, the notion of quadratic H∞ performance is introduced for a rather general class of nonlinear descriptor systems. The approach is specialized to the performance analysis and controller synthesis of descriptor systems with norm bounded uncertainties. In this case quadratic H∞ performance can be characterized by means of parameterized linear matrix inequ...