scholarly journals On the Sets of Convergence for Sequences of the -Bernstein Polynomials with

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Sofiya Ostrovska ◽  
Ahmet Yaşar Özban
Keyword(s):  
Continuous Function ◽  
Uniform Approximation ◽  
Time Scale ◽  
Bernstein Polynomials ◽  
Numerical Examples

The aim of this paper is to present new results related to the convergence of the sequence of the -Bernstein polynomials in the case , where is a continuous function on . It is shown that the polynomials converge to uniformly on the time scale , and that this result is sharp in the sense that the sequence may be divergent for all . Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

scholarly journals Density Problems in Sobolev’s Spaces on Time Scales

2021 ◽  
Vol 45 (02) ◽  
pp. 215-223
Author(s):  
AMINE BENAISSA CHERIF ◽  
FATIMA ZOHRA LADRANI
Keyword(s):  
Continuous Function ◽  
Time Scales ◽  
Time Scale ◽  
Function Spaces ◽  
First Order ◽  
Example Spaces

In this paper, we present a generalization of the density some of the functional spaces on the time scale, for example, spaces of rd-continuous function, spaces of Lebesgue Δ-integral and first-order Sobolev’s spaces.

scholarly journals The Truncatedq-Bernstein Polynomials in the Caseq>1

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mehmet Turan
Keyword(s):  
Bernstein Polynomials ◽  
Numerical Examples ◽  
Theoretical Results

The truncatedq-Bernstein polynomialsBn,m,qf;x,n∈ℕ, and  m∈ℕ0emerge naturally when theq-Bernstein polynomials of functions vanishing in some neighbourhood of 0 are considered. In this paper, the convergence of the truncatedq-polynomials on0,1is studied. To support the theoretical results, some numerical examples are provided.

How close is the approximation by Bernstein polynomials?

2020 ◽  
Vol 104 (561) ◽  
pp. 482-494
Author(s):  
G. J. O. Jameson
Keyword(s):  
Continuous Function ◽  
Bernstein Polynomials ◽  
Real Interval ◽  
Famous Theorem

A famous theorem of Weierstrass, dating from 1885, states that any continuous function can be uniformly approximated by polynomials on a bounded, closed real interval.

scholarly journals Alternative methods for solving nonlinear two-point boundary value problems

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 371-374
Author(s):  
Fateme Ghomanjani ◽  
Stanford Shateyi
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Bernstein Polynomials ◽  
Nonlinear Problems ◽  
Alternative Methods ◽  
Point Boundary ◽  
Numerical Examples ◽  
Curve Method ◽  
Linear And Nonlinear

Abstract In this sequel, the numerical solution of nonlinear two-point boundary value problems (NTBVPs) for ordinary differential equations (ODEs) is found by Bezier curve method (BCM) and orthonormal Bernstein polynomials (OBPs). OBPs will be constructed by Gram-Schmidt technique. Stated methods are more easier and applicable for linear and nonlinear problems. Some numerical examples are solved and they are stated the accurate findings.

The r-monotonicity of generalized Bernstein polynomials

2012 ◽  
Vol 55 (3) ◽  
pp. 797-807
Author(s):  
Laiyi Zhu ◽  
Zhiyong Huang
Keyword(s):  
Continuous Function ◽  
Bernstein Polynomials ◽  
Sufficient Condition ◽  
Generalized Bernstein Polynomials

AbstractLet f ∊ C[0, 1] and let the Bn(f, q; x) be generalized Bernstein polynomials based on the q-integers that were introduced by Phillips. We prove that if f is r-monotone, then Bn(f, q; x) is r-monotone, generalizing well-known results when q = 1 and the results when r = 1 and r = 2 by Goodman et al. We also prove a sufficient condition for a continuous function to be r-monotone.

scholarly journals Compactly Supported Tight and Sibling Frames Based on Generalized Bernstein Polynomials

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Ting Cheng ◽  
Xiaoyuan Yang
Keyword(s):  
Bernstein Polynomials ◽  
Approximation Order ◽  
Refinable Functions ◽  
Numerical Examples ◽  
Compactly Supported ◽  
Derived Properties ◽  
Cascade Algorithms ◽  
Generalized Bernstein Polynomials

We obtain a family of refinable functions based on generalized Bernstein polynomials to provide derived properties. The convergence of cascade algorithms associated with the new masks is proved, which guarantees the existence of refinable functions. Then, we analyze the symmetry, regularity, and approximation order of the refinable functions, which are of importance. Tight and sibling frames are constructed and interorthogonality of sibling frames is demonstrated. Finally, we give numerical examples to explicitly illustrate the construction of the proposed approach.

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