相关论文: A Bernstein-Bezier Sufficient Condition for Invert…
We show that S.Vavasis' sufficient condition for global invertibility of a polynomial mapping can be easily generalized to the case of a general Lipschitz mapping. Keywords: Invertibility conditions, generalized Jacobian, nonsmooth…
We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…
This paper introduces three sets of sufficient conditions, for generating bijective simplicial mappings of manifold meshes. A necessary condition for a simplicial mapping of a mesh to be injective is that it either maintains the orientation…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
This note considers a finite dimensional statistical model for the Calder\'on problem with piecewise constant conductivities. In this setting it is shown that injectivity of the forward map and its linearisation suffice to prove the…
We develop a new kind of nonnegativity certificate for univariate polynomials on an interval. In many applications, nonnegative Bernstein coefficients are often used as a simple way of certifying polynomial nonnegativity. Our proposed…
We formulate and discuss a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…
We give the sufficient condition on coefficients $a_k$ of an algebraic polynomial $P(z)=\sum_{k=0}^{n}a_kz^k$, $a_n\not=0,$ for the pointwise Bernstein inequality $|P'(z)|\le n|P(z)|$ to be true for all $z\in\overline{\mathbb…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
We determine a necessary and sufficient condition for a polynomial over an algebraically closed field $k$ to induce a surjective map on matrix algebras $M_n(k)$ for $n \ge 2$. The criterion is given in terms of critical points and uses…
We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement…
In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this…
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz…
This article proposes a bivariate polynomial problem for finite-order real matrices that endows a \textit{`sufficient condition'} for a map from the standard vector spaces of finite-order real matrices to the same dimensional bivariate…