Solving bivariate systems using Rational Univariate Representations
نویسندگان
چکیده
منابع مشابه
Improved algorithms for solving bivariate systems via Rational Univariate Representations
Given two coprime polynomials P and Q in Z[x, y] of degree bounded by d and bitsize bounded by τ , we address the problem of solving the system {P,Q}. We are interested in certified numerical approximations or, more precisely, isolating boxes of the solutions. We are also interested in computing, as intermediate symbolic objects, rational parameterizations of the solutions, and in particular Ra...
متن کاملSparse Rational Univariate Representation
We present explicit worst case degree and height bounds for the rational univariate representation of the isolated roots of polynomial systems based on mixed volume. We base our estimations on height bounds of resultants and we consider the case of 0-dimensional, positive dimensional, and parametric polynomial systems. CCS Concepts •Computing methodologies→ Symbolic calculus algorithms;
متن کاملReal Solving of Bivariate Polynomial Systems
We propose exact, complete and efficient methods for 2 problems: First, the real solving of systems of two bivariate rational polynomials of arbitrary degree. This means isolating all common real solutions in rational rectangles and calculating the respective multiplicities. Second, the computation of the sign of bivariate polynomials evaluated at two algebraic numbers of arbitrary degree. Our ...
متن کاملAsymmetric Univariate and Bivariate Laplace and Generalized Laplace Distributions
Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.
متن کاملBivariate interpolation based on univariate subdivision schemes
The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate ...
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: Journal of Complexity
سال: 2016
ISSN: 0885-064X
DOI: 10.1016/j.jco.2016.07.002