In this paper we establish a relation between the support of a function f on Ω1 ⊂ R with differentiability properties of its image Tf on Ω2 ⊂ R under a linear operator T . The classical approach requires analytic continuation of the image Tf from Ω2 into the complex domain C (theorems of Paley-Wiener type [5, 6, 7]), and therefore, could not apply to functions whose images Tf are not analytic a...

pn(xi,...,xn) = 0 for x = (x\,... ,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc. Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Grobner bas...

For many mechanical systems, including nearly all robotic manipulators, the set of possible configurations that the links may assume can be described by a system of polynomial equations. Thus, solving such systems is central to many problems in analyzing the motion of a mechanism or in designing a mechanism to achieve a desired motion. This paper describes techniques, based on polynomial contin...

Let {f1, f2, . . . , ft} ⊂ Q[z1, . . . , zN ] be a set of homogeneous polynomials. Let Z denote the complex, projective, algebraic set determined by the homogeneous ideal I = (f1, f2, . . . , ft) ⊂ C[z1, . . . , zN ]. Numerical continuation-based methods can be used to produce arbitrary precision numerical approximations of generic points on each irreducible component of Z. Consider the prime d...

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called ...

Abstract. Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A procedure of A. Sommese and C. Wampler consists in slicing the components with linear subspaces in general position to obtain generic points of the compo...

The multi-homogenous homotopy continuation method can solve all isolated solutions of polynomial systems. Different variable partition yields different multi-homogenous Bézout number, which gives the upper bound of the number of isolated solutions. However, the computation of the multi-homogenous Bézout number is hard. In this paper, the permanent formulation of the multi-homogenous Bézout numb...

Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution of a generic system that is used to start up the deformations. Software and applications are discussed. AMS Subject Classification. 14N10, 14M15, 52A39, 52B...

There is proposed a representation of the Drazin inverse of a given polynomial square matrix, based on the extension of the Leverrier-Faddeev algorithm. Also, an algorithm for symbolic computation of the Drazin inverse of polynomial matrix is established. This algorithm represents an extension of the papers [5], [7] and a continuation of the papers [8], [9], [10]. The implementation is develope...

Abstract. In this paper, the optimal fuel impulsive time-fixed rendezvous problem is considered. Under some simplifying assumptions, this problem may be recast as a non convex polynomial optimization problem. A numerical solving algorithm using a convex relaxation based on sum-of-squares representation of positive polynomials is proposed. Numerical results are evaluated on two examples and chec...