A new approach to improve the order of approximation of the Bernstein operators: theory and applications

DOI10.1007/s11075-017-0307-zzbMath1388.41002OpenAlexW2603925683MaRDI QIDQ679703

M. R. Eslahchi, Hassan Khosravian-Arab, Mehdi Dehghan

Publication date: 19 January 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0307-z

zbMATH Keywords

rate of convergenceBernstein theoremKorovkin theoremlinear positive operatordegree of convergencethe Bernstein operatorsVoronovkaja theorem

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Numerical integration (65D30)

Related Items (18)

Improved rate of approximation by modification of Baskakov operator ⋮ Bézier variant of modified \(\alpha\)-Bernstein operators ⋮ A spectral method based on Bernstein orthonormal basis functions for solving an inverse Roseneau equation ⋮ Modified Kantorovich operators with better approximation properties ⋮ On the shape-preserving properties of \(\lambda\)-Bernstein operators ⋮ Approximation by certain linking operators ⋮ Wavelets based computational algorithms for multidimensional distributed order fractional differential equations with nonlinear source term ⋮ On complex modified Bernstein-Stancu operators ⋮ A new representation and shape‐preserving properties of perturbed Bernstein operators ⋮ Perturbed Bernstein-type operators ⋮ Bernstein series solutions of multidimensional linear and nonlinear Volterra integral equations with fractional order weakly singular kernels ⋮ Approximation by modified Kantorovich-Stancu operators ⋮ Better numerical approximation by Durrmeyer type operators ⋮ A numerical comparative study of generalized Bernstein-Kantorovich operators ⋮ Approximation by complex perturbed Bernstein-type operators ⋮ Modified \(\alpha\)-Bernstein operators with better approximation properties ⋮ Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties ⋮ Modifiedρ-Bernstein Operators for Functions of Two Variables

Cites Work

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• Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bézier curves
• An answer to a conjecture on Bernstein operators
• On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations
• On the convergence of derivatives of Bernstein approximation
• The complete asymptotic expansion for Bernstein operators
• On simultaneous approximation for some modified Bernstein-type operators
• Interpolation and approximation by polynomials
• The saturation class and iterates of the Bernstein polynomials
• Asymptotic expansion and extrapolation for Bernstein polynomials with applications
• Convergence Estimates in Approximation Theory
• Linear Combinations of Bernstein Polynomials

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