Related papers: Superposition, reduction of multivariable problems…

Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…

We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…

This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…

Every one knows that an equation is equivalent to a multivariate function. Generally speaking, there are more than one unknown x in this multivariate function and it is not easy to reduce the number of unknown x to one. In this paper we…

The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

The paper considers a symbolic approach to Prony's method in several variables and its close connection to multivariate polynomial interpolation. Based on the concept of universal interpolation that can be seen as a weak generalization of…

We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized…

Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…

We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…

Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…

Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…

This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…

This research introduces a new method for the transition from partial to ordinary differential equations that is based on the Kolmogorov superposition theorem. In this paper, we discuss the numerical implementation of the Kolmogorov theorem…

In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…