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A linear programming based analysis of the CP-rank of completely positive matrices

Yingbo Li, Anton Kummert, Andreas Frommer (2004)

International Journal of Applied Mathematics and Computer Science

A real matrix A is said to be completely positive (CP) if it can be decomposed as A = BB^T, where the real matrix B has exclusively non-negative entries. Let k be the rank of A and Φ_k the least possible number of columns of the matrix B, the so-called completely positive rank (cp-rank) of A. The present work is devoted to a study of a general upper bound for the cp-rank of an arbitrary completely positive matrix A and its dependence on the ordinary rank k. This general upper bound of the cp-rank...

A lower bound sequence for the minimum eigenvalue of Hadamard product of an M -matrix and its inverse

Wenlong Zeng, Jianzhou Liu (2022)

Czechoslovak Mathematical Journal

We propose a lower bound sequence for the minimum eigenvalue of Hadamard product of an M -matrix and its inverse, in terms of an S -type eigenvalues inclusion set and inequality scaling techniques. In addition, it is proved that the lower bound sequence converges. Several numerical experiments are given to demonstrate that the lower bound sequence is sharper than some existing ones in most cases.

A matrix constructive method for the analytic-numerical solution of coupled partial differential systems

Lucas Jódar, Enrique A. Navarro, M. V. Ferrer (1995)

Applications of Mathematics

In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation u t - A u x x - B u = 0 , where B is an arbitrary square complex matrix and A ia s matrix such that the real part of the eigenvalues of the matrix 1 2 ( A + A H ) is positive. Given an admissible error ε and a finite domain G , and analytic-numerical solution whose error is uniformly upper bounded by ε in G , is constructed.

A matrix derivation of a representation theorem for (tr Ap)1/p.

Heinz Neudecker (1989)

Qüestiió

A matrix derivation of a well-known representation theorem for (tr Ap)1/p is given, which is the solution of a restricted maximization problem. The paper further gives a solution of the corresponding restricted minimization problem.

A modified Cayley transform for the discretized Navier-Stokes equations

K. A. Cliffe, T. J. Garratt, Alastair Spence (1993)

Applications of Mathematics

This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...

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