相关论文: On Tractability of Approximation for a Special Spa…
Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$,…
Working notes on setting up approximate dynamical systems and nonlinear eigenvalue problems, here embedded within the theory of complex nonlinear dynamics. Computations parallel those of linear quantum theory except that we use functional…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
We study the integration and approximation problems for monotone and convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
We study the random sampling of band-limited functions of several variables. If a bandlimited function with bandwidth one has its essential support on a cube of volume $R^d$, then $\cO (R^d \log R^d)$ random samples suffice to approximate…
We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak…
We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is…
We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…
An efficient approach for the construction of separable approximations of optimal value functions from interconnected optimal control problems is presented. The approach is based on assuming decaying sensitivities between subsystems,…
The sampling of functions of bounded variation (BV) is a long-standing problem in op- timization. The ability to sample such functions has relevance in the field of variational inverse problems, where the standard theory fails to guarantee…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
In the real world, insufficient information, limited computation resources, and complex problem structures often force an autonomous agent to make a decision in time less than that required to solve the problem at hand completely. Flexible…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…