相关论文: A Mathematica program for numerically computing re…

We obtain precise plateau estimates for the two-point function of the finite-volume weakly-coupled hierarchical $|\varphi|^4$ model in dimensions $d \ge 4$, for both free and periodic boundary conditions, and for any number $n \ge 1$ of…

In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…

Floating point error is a drawback of embedded systems implementation that is difficult to avoid. Computing rigorous upper bounds of roundoff errors is absolutely necessary for the validation of critical software. This problem of computing…

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…

We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…

Let $\mathbf{f} = \left(f_1, \dots, f_p\right) $ be a polynomial tuple in $\mathbb{Q}[z_1, \dots, z_n]$ and let $d = \max_{1 \leq i \leq p} \deg f_i$. We consider the problem of computing the set of asymptotic critical values of the…

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…

Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are: the affine critical values, the affine Milnor numbers for all irregular fibers, the…

We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the…

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…

In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…

We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on $\delta$-generic…

Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…

The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…

General relativistic Riemann solvers are typically complex, fragile and unwieldy, at least in comparison to their special relativistic counterparts. In this paper, we present a new high-resolution shock-capturing algorithm on curved…

We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework that encompasses continuous, discrete, and hybrid settings.…

We provide a systematic study of boundary data maps, that is, 2 \times 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrodinger operators on a compact interval [0,R] with…

We present the Mathematica package SpinorHelicity4D, a dedicated suite for analytic and numeric calculations involving four-dimensional massless and massive spinor-helicity formalism. Analytic features of the package include for example:…