The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...

Given two ellipsoids, we show that their characteristic equation has at least two negative roots and that the ellipsoids are separated by a plane if and only if their characteristic equation has two distinct positive roots. Furthermore, the ellipsoids touch each other externally if and only if the characteristic equation has a positive double root. An advantage of this characterization is that ...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

In this paper an algebraic test procedure is presented to ascertain the stability of multidimensional discrete systems, which are represented in the forms of their respective characteristic equations. Further an equivalent single dimensional characteristics equation is formed for the given multidimensional characteristic equation; the coefficients of this characteristic equation are suitably ar...

The GeometricXL algorithm is a geometrically invariant version of the XL algorithm that uses polynomials of a much smaller degree than either a standard Groebner basis algorithm or an XL algorithm for certain multivariate equation systems. However, the GeometricXL algorithm as originally described is not well-suited to fields of even characteristic. This paper discusses adaptations of the Geome...

We study characteristic schemes for a model problem for the Fermi pencil beam equation. The objective is twofold: (i) To design eecient and accurate numerical schemes based on the principle of solving a particle transport problem, exactly, on each collision free spatial segment combined with a projection on each collision site, from a pre collision angle and energy coordinates (AE) to a post co...

Efficient characteristic set methods for computing solutions of a polynomial equation system in a finite field is proposed. We introduce the concept of proper triangular sets and prove that proper triangular sets are square-free in certain sense. We present an improved algorithm which can be used to reduce the zero set of an equation system in general form as the union of zero sets of proper tr...

The paper presents a method for constructing the characteristic equation of SISO linear periodic dynamical systems with distributed delay. The construction bases on a description in frequency domain, and a relation between the characteristic function of the periodic system and the Fredholm denominator of an associated Fredholm integral equation of the second kind. Using the Fredholm calculus, p...