Simultaneous Approximation and Interpolation of Functions on Continua in the Complex Plane
نویسندگان
چکیده
We construct polynomial approximations of Dzjadyk type (in terms of the k -th modulus of continuity, k ≥ 1 ) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E . Furthermore, the error in this approximation is decaying as e−cn α strictly inside E , where c and α are positive constants independent of the degree n of the approximating polynomial.
منابع مشابه
Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions
Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.
متن کاملApproximation of a Fuzzy Function by Using Radial Basis Functions Interpolation
In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...
متن کاملNumerical Simulation of 1D Linear Telegraph Equation With Variable Coefficients Using Meshless Local Radial Point Interpolation (MLRPI)
In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines ...
متن کاملMultiple cracks in an elastic half-plane subjected to thermo-mechanical loading
An analytical solution is presented for the thermoelastic problem of a half-plane with several cracks under thermo mechanical loading using distributed dislocation technique. The uncoupled quasi-static linear thermoelasticity theory is adopted in which the change in temperature, if any, due to deformations is neglected. The stress field in a half-plane containing thermoelastic dislocation is ob...
متن کاملScattered data approximation of fully fuzzy data by quasi-interpolation
Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$. In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...
متن کامل