We discuss the eigenvalue problem for general and structured matrix polynomials which may be singular and may have eigenvalues at infinity. We derive condensed forms that allow (partial) deflation of the infinite eigenvalue and singular structure of the matrix polynomial. The remaining reduced order staircase form leads to new types of linearizations which determine the finite eigenvalues and c...

This paper describes a model for concurrent computation based on single-writer single-assignment variables. The description is primarily graphical, resembling the interaction nets formalism. The model embodies rules in a process which may require two or more communications from other processes to respond. However, these are managed by a partial evaluation response on receiving a single communic...

In this paper, we consider the partial inverse assignment problem under l1 norm without bound constraints. We show that the partial inverse problem can be solved by a strongly polynomial algorithm. The technique for solving this problem can be extended to handle a special type of partial inverse 0.1 combinatorial optimization problems. © 2006 Elsevier B.V. All rights reserved.

The aim of the book is to provide an analysis of the boundary element method for the numerical solution of Laplacian eigenvalue problems. The representation of Laplacian eigenvalue problems in the form of boundary integral equations leads to nonlinear eigenvalue problems for related boundary integral operators. The solution of boundary element discretizations of such eigenvalue problems require...

In this paper, we improve a result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a (1−ε)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignment satisfying at least a 1 − Cε/hG fraction of all constraints if ε < cλG where hG is the edge expansion of G, λG is the second smallest eigenvalue...

The studied linear discrete-continuous system contains two coupled subsystems: one with continuous-time dynamics, the other with discrete-time dynamics. Continuoustime dynamics are described by ordinary linear differential equations, whereas discretetime dynamics are described by difference equations for the system state jumps at prescribed time instants. Systems of three following degrees of g...

The quadratic assignment problem (denoted QAP), in the trace formulation over the permutation matrices, is min X2 tr(AXB + C)X t : Several recent lower bounds for QAP are discussed. These bounds are obtained by applying continuous optimization techniques to approximations of this combinatorial optimization problem, as well as by exploiting the special matrix structure of the problem. In particu...

This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pe...