We show how one can use non-prime-power, composite moduli for computing representations of the product of two n × n matrices using only n multiplications and additions.

We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time...

Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program. A nite criss-cross method, based on least{index resolution, is constructed for solving the LCP. In proving nitenes...

We exhibit an explicit formula for the cardinality of solutions to a class quadratic matrix equations over finite fields. prove that orbits these under natural conjugation action general linear groups can be separated by classical invariants defined characteristic polynomials. also find generating set vanishing ideal orbits.

The paper establishes the design procedure for the state feedback control of linear discrete-time systems, considerable as an interposed design criterium in the form of linear matrix inequalities. The goal is to design the feedback control which guarantees bounded H2 performance index for the system transfer function matrix and H∞ norm attenuation for the disturbance transfer function matrix, b...

Given a pair of distinct eigenvalues (λ1, λ2) of an n×n quadratic matrix polynomial Q(λ) with nonsingular leading coefficient and their corresponding eigenvectors, we show how to transform Q(λ) into a quadratic of the form [ Qd(λ) 0 0 q(λ) ] having the same eigenvalues as Q(λ), with Qd(λ) an (n− 1)× (n− 1) quadratic matrix polynomial and q(λ) a scalar quadratic polynomial with roots λ1 and λ2. ...

In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

Quadratically constrained quadratic programs (QQPs) play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Lagrangian relaxations often provide good approximate solutions to these hard problems. Such relaxations are equivalent to semidefinite programming relaxations. For several special cases of QQP, e.g., convex programs an...

Nonnegative Matrix Factorization (NMF) solves the following problem: find such nonnegative matrices A ∈ RI×J + and X ∈ RJ×K + that Y ∼= AX, given only Y ∈ RI×K and the assigned index J (K >> I ≥ J). Basically, the factorization is achieved by alternating minimization of a given cost function subject to nonnegativity constraints. In the paper, we propose to use Quadratic Programming (QP) to solv...