Related papers: Computing planar and spherical choreographies
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
The runtime analysis of decentralised software requires instrumentation methods that are scalable, but also minimally invasive. This paper presents a new algorithm that instruments choreographed outline monitors. Our instrumentation…
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…
We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in $\mathbb{R}^n$ and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such…
The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation…
We consider polynomials of a few linear forms and show how exploit this type of sparsity for optimization on some particular domains like the Euclidean sphere or a polytope. Moreover, a simple procedure allows to detect this form of…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…
We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…
The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical…
In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…
Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…