On Jackson-type inequalities associated with separable Haar wavelets

2016 ◽  
Vol 14 (03) ◽  
pp. 1650005 ◽  
Author(s):  
P. Andrianov ◽  
M. Skopina
Keyword(s):  
Uniform Approximation ◽  
Sharp Estimate ◽  
Type Inequality ◽  
Haar Wavelets ◽  
Jackson Type ◽  
Periodic Functions ◽  
Interesting Phenomenon

Uniform approximation of multivariate periodic functions by Haar polynomials is studied. A general sharp Jackson type inequality and its refinement for certain types of numbers [Formula: see text] are discussed. An interesting phenomenon appears for some numbers [Formula: see text]: a sharp estimate is not unique.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

Exact inequalities of jackson type for periodic functions in space L2

1988 ◽  
Vol 43 (6) ◽  
pp. 435-443 ◽  
Author(s):  
A. A. Ligun
Keyword(s):  
Jackson Type ◽  
Periodic Functions

scholarly journals Convexity, moduli of smoothness and a Jackson-type inequality

2010 ◽  
Vol 130 (3) ◽  
pp. 254-285 ◽  
Author(s):  
Z. Ditzian ◽  
A. Prymak
Keyword(s):  
Type Inequality ◽  
Moduli Of Smoothness ◽  
Jackson Type

scholarly journals Multivariate Jackson-type inequality for a new type neural network approximation

2014 ◽  
Vol 38 (24) ◽  
pp. 6031-6037 ◽  
Author(s):  
Shaobo Lin ◽  
Yuanhua Rong ◽  
Zongben Xu
Keyword(s):  
Neural Network ◽  
Type Inequality ◽  
Jackson Type ◽  
New Type

Max-Product Shepard Approximation Operators

2006 ◽  
Vol 10 (4) ◽  
pp. 494-497 ◽  
Author(s):  
Barnabás Bede ◽  
◽  
Hajime Nobuhara ◽  
János Fodor ◽  
Kaoru Hirota ◽  
...  
Keyword(s):  
Error Estimate ◽  
Approximation Theory ◽  
Uniform Approximation ◽  
Approximation Theorem ◽  
Jackson Type ◽  
Approximation Operators

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.

scholarly journals Approximation of functions and their conjugates in Lp and uniform metric by Euler means

2018 ◽  
Vol 51 (1) ◽  
pp. 141-150
Author(s):  
Sergey S. Volosivets ◽  
Anna A. Tyuleneva
Keyword(s):  
Uniform Approximation ◽  
Conjugate Functions ◽  
Periodic Functions ◽  
Best Approximations ◽  
Approximation Of Functions

Abstract For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.

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