Related papers: On Better Approximation Order for the Nonlinear q-…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
Here we study the approximation properties of a modified Goodman-Sharma operator recently considered by Acu and Agrawal in 2019. This operator is linear but not positive. It has the advantage of a higher order of approximation of functions…
Herein we propose a complex form of a genuine Bernstein-Durrmeyer type operators depending on a non-negative real parameter $\alpha.$ We present the quantitative upper bound, Voronovskaja type result and exact order of approximation for…
In the present study, we have given a corrigendum to our paper on the approximation properties of bivariate $(p, q)-$Bernstein operators. Recently, we \cite{kar} have defined the bivariate $(p, q)-$Bernstein operators. Later, we have aware…
In this study, we consider the application of max-plus-linear approximators for Q-function in offline reinforcement learning of discounted Markov decision processes. In particular, we incorporate these approximators to propose novel fitted…
Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn…
The emphasis of this paper is to investigate the high-order approximation of a class of SPDEs with cubic nonlinearity driven by multiplicative noise with the help of the amplitude equations. The highlight of our work is that we improve the…
The $\alpha$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis…
We study nonlinear approximation in $\operatorname{BMO}$ from splines generated by a hierarchy of B-splines over regular multilevel nested partitions of $\mathbb R$. Companion Jackson and Bernstein estimates are established that allow to…
This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics…
In the present article, we have given a corrigendum to our paper "Some approximation results on Bernstein-Schurer operators defined by (p,q)-integers" published in Journal of In- equalities and Applications (2015) 2015:249.
The concept of quantum-mechanical nematic order, which is important in systems such as superconductors, is based on an analogy to classical liquid crystals, where order parameters are obtained through orientational expansions. We generalize…
For operators representing ill-posed problems, an ordering by ill-posedness is proposed, where one operator is considered more ill-posed than another one if the former can be expressed as a cocatenation of bounded operators involving the…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
This article discusses the convergence properties of the Max Product and Max Min variants of Durrmeyer type exponential sampling series. We first establish pointwise and uniform convergence of both operators in the space of log uniformly…
In this paper, we have given a corrigendum to our paper "Some Approximation Results by $(p,q)$-analogue of Bernstein-Stancu Operators" published in Applied Mathematics and Computation $264 (2015) 392-402.$ We introduce a new analogue of…
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the…
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum…
Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of…