Computing real witness points of positive dimensional polynomial systems
نویسندگان
چکیده
منابع مشابه
Computing real witness points of positive dimensional polynomial systems
We consider a critical point method for finding certain solution (witness) points on real solution components of real polynomial systems of equations. The method finds points that are critical points of the distance from a plane to the component with the requirement that certain regularity conditions are satisfied. In this paper we analyze the numerical stability and complexity of the method. W...
متن کاملComputing the Least Fixed Point of Positive Polynomial Systems
We consider equation systems of the form X1 = f1(X1, . . . , Xn), . . . , Xn = fn(X1, . . . , Xn) where f1, . . . , fn are polynomials with positive real coefficients. In vector form we denote such an equation system by X = f(X) and call f a system of positive polynomials, short SPP. Equation systems of this kind appear naturally in the analysis of stochastic models like stochastic context-free...
متن کاملAdaptive Compensators for Perturbed Positive Real Infinite-dimensional Systems
The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinitedimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law bas...
متن کاملNumerically computing real points on algebraic sets
Given a polynomial system f , a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at...
متن کاملOn points at infinity of real spectra of polynomial rings
Let R be a real closed field and A = R[x1, . . . , xn]. Let Sper A denote the real spectrum of A. There are two kinds of points in Sper A: finite points (those for which all of |x1|,. . . ,|xn| are bounded above by some constant in R) and points at infinity. In this paper we study the structure of the set of points at infinity of Sper A and their associated valuations. Let T be a subset of {1, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2017
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2017.03.035