Related papers: Computing Birational Polynomial Surface Parametriz…

In this paper, we construct an algorithm for minimising piecewise smooth functions for which derivative information is not available. The algorithm constructs a pair of quadratic functions, one on each side of the point with smallest known…

We give a necessary and sufficient condition for an automorphism of the Hilbert scheme of points on a K3 surface (non necessarily algebraic) to be induced by an automorphism of the surface. We prove furthermore that the group of birational…

In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…

We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that…

We classify finite groups acting by birational transformations of a non-trivial Severi--Brauer surface over a field of characteristc zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism…

We study degree two unirational parameterizations of geometrically rational surfaces over the real field.

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

Inferring signed distance functions (SDFs) from sparse point clouds remains a challenge in surface reconstruction. The key lies in the lack of detailed geometric information in sparse point clouds, which is essential for learning a…

Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…

We adapt an old local-to-global technique of Ore to compute, under certain mild assumptions, an integral basis of a number field without a previous factorization of the discriminant of the defining polynomial. In a first phase, the method…

In this paper, we presents a method for factoring morphisms between arithmetic surfaces based on the regularity of arithmetic surfaces. Using this factorization, we derive a Riemann-Hurwitz formula satisfied by the ramification divisor and…

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…

One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…

For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…

A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…

Given the equations of the first and the second order surfaces in multidimensional space, our goal is to construct a univariate polynomial one of the zeros of which coincides with the square of the distance between these surfaces. To…

We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general positions. As an application we obtain a classification of special linear systems on P1xP1 for which the multiplicities…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…