相关论文: Max-Min Representation of Piecewise Linear Functio…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand,…
In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Every CPWL function has infinitely many such decompositions,…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.
We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
Using linear projections one gets new inequalities for the successive minima of the lattice of sections of an hermitian line bundle on an arithmetic surface.
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…
Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all common activations, value functions of mixed-integer…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).
The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice…
Let $\mathbb{F}_p$ be the finite field of prime order $p$. For any function $f \colon \mathbb{F}_p{}^n \to \mathbb{F}_p$, there exists a unique polynomial over $\mathbb{F}_p$ having degree at most $p-1$ with respect to each variable which…
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite…
In this paper we consider polynomial representability of functions defined over $Z_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
We show that the set of max-plus measures representing a given max-plus harmonic vector has a least element. This may be viewed as an analogue of the uniqueness of the integral representation of harmonic functions in Potential Theory. As an…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…