相关论文: Some Remarks on a General Construction af Approxim…
Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
This paper shows that how to approximate general fuzzy number by using convolution method.
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
This article develops an approximate proximal approach for the generalized method of lines. The present results are extensions and applications of previous ones which have been published since 2011, in books and articles such as [3,4,5,6].…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
Approximation of entire functions by their pad\'e approximants has been examined in the past. It is true that generically such an approximation holds. However, examining this problem from another viewpoint, we obtain stronger generic…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We describe general heuristics to approximately solve a wide variety of problems with convex objective and decision variables from a nonconvex set. The heuristics, which employ convex relaxations, convex restrictions, local neighbor search…
It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Compositional generalization is the capacity to recognize and imagine a large amount of novel combinations from known components. It is a key in human intelligence, but current neural networks generally lack such ability. This report…
Aggregating different pieces of similar information is necessary to generate concise and easy to understand reports in technical domains. This paper presents a general algorithm that combines similar messages in order to generate one or…
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
We propose a generalization of the method of cyclic projections, which uses the lengths of projection steps carried out in the past to learn about the geometry of the problem and decides on this basis which projections to carry out in the…
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…