Related papers: Taylor approximations of operator functions
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
We consider perturbed eigenvalue problems of the 1-Laplace operator and verify the existence of a sequence of solutions. It is shown that the eigenvalues of the perturbed problem converge to the corresponding eigenvalue of the unperturbed…
This paper deals with the modified q-Stancu-Beta operators and we have investigated the statistical approximation theorems for these operators with the help of the Korovkin type approximation theorem. We have also established the rates of…
We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford-Taylor integral approach. We use a sinc quadrature scheme to approximate the Balakrishnan representation of the negative…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…
We survey the classical results of the Dirichlet Approximation Theorem.
In this paper, we are dealing with a new type of Baskakov-Schurer-Szasz operators (\ref{eq1}). Approximation properties of this operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the…
We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator $L$ defined to be the unbounded operator associated with a Hermitian, coercive and bounded sesquilinear form on…
Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer the problem of uniform approximation of continuous functions on closed bounded interval and the problem of…
Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…
Recent lattice calculations of hadron structure functions are described.
In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and…
In this note a general approach is suggested for comparison of operators. This is done by means of the Fourier transform of a measure. This approach is applied to comparison of approximation properties of various summability methods of the…
In this paper, several modifications are introduced to the functional approximation method iterLap to reduce the approximation error, including stopping rule adjustment, proposal of new residual function, starting point selection for…