Related papers: Taylor approximations of operator functions
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally,…
In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.
This thesis explores a number of online machine learning algorithms. From a theoret- ical perspective, it assesses their employability for a particular function approximation problem where the analytical models fall short. Furthermore, it…
We prove the existence of entire functions that achieve universal approximations on certain countable sequences of translation operators .
In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such…
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schr\"odinger operators. It provides more details and suitable extensions to already existing results, that are needed in other…
This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason's seminal paper in 2007.
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
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…
In arXiv:1306.2914 a method for approximate solution of Sturm-Liouville equations and related spectral problems was presented based on the construction of the Delsarte transmutation operators. The problem of numerical approximation of…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…
We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…
This is a continuation of our earlier paper \cite{PT3}. We consider here operator-valued functions (or infinite matrix functions) on the unit circle $\T$ and study the problem of approximation by bounded analytic operator functions. We…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…
In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…