A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions [PDF]
, 2008 We study polynomial approximations of vertex singularities of the type $r^\lambda |\log r|^\beta$ on three-dimensional surfaces. The analysis focuses on the case when $\lambda > -\frac 12$.
Bespalov, A, Bespalov, Alexei
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On polynomial approximation in the complex plane with application to conformal mapping [PDF]
Mathematics of Computation, 1985 We consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane. While a monomial basis may be very ill-conditioned, we show that a basis of Lagrange polynomials with Fejér points as nodes is well-conditioned.
Lothar Reichel
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A Class of Quadrature Rules for Complex Cauchy Principal Value Integrals [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2023 This article is fully devoted to the numerical approximation of Cauchy-type integrals in the complex plane. A class of degree eight quadrature rules is formulated from a family of Gauss-type two-point rules based on the method of extrapolation. The basic
Arup Kumar Saha +2 more
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A numerical method for the computation of faber polynomials for starlike domains [PDF]
, 1991 We describe a simple numerical process (based on the Theodorsen method for conformal mapping ) for computing approximations to Faber polynomials for starlike ...
Soares, M J +2 more
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The GW/BSE Method in Magnetic Fields
Frontiers in Chemistry, 2021 The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field.
Christof Holzer +3 more
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On a Class of Positive Definite Operators and Their Application in Fractional Calculus
Axioms, 2022 This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated.
Temirkhan Aleroev
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\(\mathcal{K}\)-FUNCTIONALS AND EXACT VALUES OF \(n\)-WIDTHS IN THE BERGMAN SPACE
Ural Mathematical Journal, 2017 In this paper, we consider the problem of mean-square approximation of complex variables functions which are regular in the unit disk of the complex plane. We obtain sharp estimates of the value of the best approximation by algebraic polynomials in terms
Mukim S. Saidusaynov
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The Approximation of Laplace-Stieltjes Transforms Concerning Sun’s Type Function
Journal of Function Spaces, 2021 The main aim of this paper is to establish some theorems concerning the error EnF,β, the Sun’s type function Ur, and Muσ,F of entire functions defined by Laplace-Stieltjes transforms with infinite order converge in the whole complex plane.
Xia Shen, Hong Yan Xu
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ON ENTIRE FUNCTIONS WITH GIVEN ASYMPTOTIC BEHAVIOR
Проблемы анализа, 2018 We study approximation of subharmonic functions on the complex plane by logarithms of moduli of entire functions. In the theory of series of exponentials these entire functions are the main tool.
Isaev K . P .
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On approximation of two-dimensional potential and singular operators [PDF]
E-Journal of Analysis and Applied Mathematics, 2019 The purpose of this paper is the construction of second-order of accuracy quadrature formulas for the numerical calculation of the Vekua types two-dimensional potential and singular integral operators in the unit disk of complex plane.
Charyyar Ashyralyyev, Sedanur Efe
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