相关论文: Implicitization using approximation complexes

We study approximation of functions by algebraic polynomials in the H\"older spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By using modifications of the classical moduli of…

Formalization of mathematics is a major topic, that includes in particular numerical analysis, towards proofs of scientific computing programs. The present study is about the finite element method, a popular method to numerically solve…

We describe a `discretize-then-relax' strategy to globally minimize integral functionals over functions $u$ in a Sobolev space subject to Dirichlet boundary conditions. The strategy applies whenever the integral functional depends…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are…

This expository article proves some results of Ferguson, on the approximation of continuous functions on a compact subset of R by polynomials with integral coefficients.

We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the essential combinatorial structure exhibited by simplexes, cubes…

This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…

We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study…

In this paper, we rigorously study an order 2 scheme that was previously proposed by some of the authors. A slight modification is proposed that enables us to prove the convergence of the scheme while simplifying in the same time the inner…

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…

A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex…

Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…

In this paper we continue the work on implicit-explicit (IMEX) time discretizations for the incompressible Oseen equations that we started in \cite{BGG23} (E. Burman, D. Garg, J. Guzm\`an, {\emph{Implicit-explicit time discretization for…

We derive an implicit description of the image of a semialgebraic set under a birational map, provided that the denominators of the map are positive on the set. For statistical models which are globally rationally identifiable, this yields…

While teaching a course on integral equations, I noticed that a straightforward combination of Neumann series and Fourier series for the resolvent (or the solution) of an integral equation has good approximation qualities. This short…

We establish an effective improvement on the Liouville inequality for approximation to complex non-real algebraic numbers by quadratic complex algebraic numbers.

Self-supervised temporal sequence alignment can provide rich and effective representations for a wide range of applications. However, existing methods for achieving optimal performance are mostly limited to aligning sequences of the same…

We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…

We present Bicoq3, a deep embedding of the B system in Coq, focusing on the technical aspects of the development. The main subjects discussed are related to the representation of sets and maps, the use of induction principles, and the…