Related papers: Addition via reduction algorithm on trigonal curve…
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly given function, we reformulate finding a best Linear/Ridge…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We show that there exists a surjection from the set of effective divisors of degree $g$ on a tropical curve of genus $g$ to its Jacobian by using a tropical version of the Riemann-Roch theorem. We then show that the restriction of the…
We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less o equal to 4 and they are defined over an algebraically closed field of characteristic zero. In addition, we also…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
Given a family of rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (${\Bbb R}$, in general) so that the shape of the family…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
Let C be an arbitrary smooth algebraic curve of genus g over a large finite field K. We revisit fast addition algorithms in the Jacobian of C due to Khuri-Makdisi (math.NT/0409209, to appear in Math. Comp.). The algorithms, which reduce to…
We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
We compute the class of a divisor on M_{g,n} given as the closure of the locus of smooth pointed curves [C; x_1,..., x_n] for which \sum d_j x_j has an effective representative, where d_j are integers summing up to g-1, not all positive.…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…
An effective method of computing division polynomials in terms of Mumford coordinates is presented. As an example, division polynomials for $3$- and $4$-torsion divisors on a genus two curve are obtained explicitly in terms of Mumford…
Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of…
Assuming GRH, we present an algorithm which inputs a prime $p$ and outputs the set of fundamental discriminants $D<0$ such that the reduction map modulo a prime above $p$ from elliptic curves with CM by $\order_{D}$ to supersingular…