相关论文: On a general approach to some problems of approxim…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…
Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast…
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…
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].…
In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
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…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…
In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In this paper we introduce the Stancu type generalization of the q-Bernstein-Schurer-Kantorovich operators and examine their approximation properties. We investigate the convergence of our operators with the help of the Korovkin's…
In this paper, using the concept of $A$-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a function $f$ by means…
In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Holder continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the…