Related papers: Equisingular calculations for plane curve singular…
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…
We give a simple algorithm showing that the reduction of the multiplicity of a characteristic p>0 hypersurface singularity along a valuation is possible if there is a finite linear projection which is defectless. The method begins with the…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
In this work we study the \emph{Saito number} of a plane curve and we present a method to determine the minimal Saito number for plane curves in a given equisingularity class, that gives rise to an actual algorithm. In particular…
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that this motion could be computed numerically by using a…
In (Arnold, 1985), V.I. Arnold has obtained normal forms and has developed a classifier for, in particular, all isolated hypersurface singularities over the complex numbers up to modality 2. Building on a series of 105 theorems, this…
In this paper, we describe a new hybrid algorithm for computing all singular triplets above a given threshold and provide its implementation in MATLAB/Octave and R. The high performance of our codes and ease at which they can be used,…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
While the tangent space to an equisingular family of curves can be discribed by the sections of a twisted ideal sheaf, this is no longer true if we only prescribe the multiplicity which a singular point should have. However, it is still…
Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare characteristic under deformation, it is applied here to compute…
We suggest an invariant way to enumerate nodal and nodal-cuspidal real deformations of real plane curve singularities. The key idea is to assign Welschinger signs to the counted deformations. Our invariants can be viewed as a local version…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a $d^{p+q}$-dimensional matrix variable that…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach,…
The polar decomposition for a matrix $A$ is $A=UB$, where $B$ is a positive Hermitian matrix and $U$ is unitary (or, if $A$ is not square, an isometry). This paper shows that the ability to apply a Hamiltonian $\pmatrix{ 0 & A^\dagger \cr A…
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of…