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.

COMPACTLY SUPPORTED MULTIVARIATE, PAIRS OF DUAL WAVELET FRAMES OBTAINED BY CONVOLUTION

2008 ◽  
Vol 06 (02) ◽  
pp. 183-208 ◽  
Author(s):  
MARTIN EHLER
Keyword(s):  
Approximation Order ◽  
Refinable Functions ◽  
Wavelet Frames ◽  
Refinable Function ◽  
Vanishing Moments ◽  
Wavelet System ◽  
Compactly Supported ◽  
Mask Size ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

In this paper, we present a construction of compactly supported multivariate pairs of dual wavelet frames. The approach is based on the convolution of two refinable distributions. We obtain smooth wavelets with any preassigned number of vanishing moments. Their underlying refinable function is fundamental. In the examples, we obtain symmetric wavelets with small support from optimal refinable functions, i.e. the refinable function has minimal mask size with respect to smoothness and approximation order of its generated multiresolution analysis. The wavelet system has maximal approximation order with respect to the underlying refinable function.

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.

Generalized Bernstein Polynomials

2004 ◽  
Vol 44 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Stanisław Lewanowicz ◽  
Paweł Woźny
Keyword(s):  
Bernstein Polynomials ◽  
Generalized Bernstein Polynomials

scholarly journals A generalization of the Bernstein polynomials

1999 ◽  
Vol 42 (2) ◽  
pp. 403-413 ◽  
Author(s):  
Haul Oruç ◽  
George M. Phillips ◽  
Philip J. Davis
Keyword(s):  
Bernstein Polynomials ◽  
Classical Case ◽  
Geometric Progression ◽  
Generalized Bernstein Polynomials

This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that, when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.

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.

scholarly journals Convergence of Generalized Bernstein Polynomials

2002 ◽  
Vol 116 (1) ◽  
pp. 100-112 ◽  
Author(s):  
Alexander Il'inskii ◽  
Sofiya Ostrovska
Keyword(s):  
Bernstein Polynomials ◽  
Generalized Bernstein Polynomials
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