We identify and analyse obstructions to factorisation of integer matrices into products NTN or N2 with rational entries. The arise as quadratic forms coefficients raise the question discrete range such forms. They are obtained by considering matrix decompositions over a superalgebra. further obtain formula for determinant square in terms adjugates these decompositions, well identifying co-Latin...

In this paper novel CNN based multiuser detection algorithms are proposed which can provide high performance mobile communication. Multiuser detection in CDMA system come down to quadratic optimization. CNNs are capable of fast quadratic optimization when the quadratic form arising from the detection problem is generated by a sparse matrix. Since multiuser communication under heavy loaded scena...

Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n × n quadratic matrix equation X − L1X − L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear s...

New relationships are enlightened between various quadratic matrix inequality conditions for stability of a scalar polynomial. It is namely shown how a recently published linear matrix inequality condition can be derived from Hermite and Lya-punov stability criteria.

The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much attention since early 1990’s. It is now understood that, under the primal Slater condition, (QP1QC) has a tight SDP relaxation (PSDP). The optimal solution to (QP1QC), if exists, can be obtained by a matrix rank one decomp...

Abstract: This paper discusses the quadratic stability and quadratic stabilization problem for a class of nonlinear perturbed discrete time-delay systems. Necessary and sufficient conditions for quadratic stability are presented via S-procedure technique and linear matrix inequality (LMI). Both static and dynamic output feedback controllers are constructed respectively. Furthermore, necessary a...

A, B, C = state-space matrices a = acceleration due to linear-quadratic-regulatorand artificial-potential-field-determined control effort aAPF = acceleration due to artificial-potential-fielddetermined control effort aLQR = acceleration due to linear-quadratic-regulatordetermined control effort am = maximum acceleration aobs = acceleration of chaser spacecraft toward an obstacle ax;y;z = accele...

We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algor...

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagon...