Related papers: Approximate Implicitization of Triangular B\'ezier…
Neural implicit modeling permits to achieve impressive 3D reconstruction results on small objects, while it exhibits significant limitations in large indoor scenes. In this work, we propose a novel neural implicit modeling method that…
The approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case of Bernstein-Bezoutian matrices constructed when the polynomials are given in…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.
Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…
We consider surface area approximations by Lagrange and Crouzeix--Raviart interpolations on triangulations. For Lagrange interpolation, we give an alternative proof for Young's classical result that claims the areas of inscribed polygonal…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we…
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…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…
Shape reconstruction from imaging volumes is a recurring need in medical image analysis. Common workflows start with a segmentation step, followed by careful post-processing and,finally, ad hoc meshing algorithms. As this sequence can be…
This paper deals with three technical ingredients of geometry for quantum information. Firstly, we give an algorithm to obtain diagonal basis matrices for submodules of the Z_{d}-module Z_{d}^{n} and we describe the suitable computational…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
In this paper we develop the isogeometric B\'ezier dual mortar method. It is based on B\'ezier extraction and projection and is applicable to any spline space which can be represented in B\'ezier form (i.e., NURBS, T-splines, LR-splines,…
In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We…
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…
An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set…