Exact bounds for the uniform approximation of continuous periodic functions by r-th order splines

1973 ◽  
Vol 13 (2) ◽  
pp. 130-136 ◽  
Author(s):  
A. A. Zhensykbaev
Keyword(s):  
Uniform Approximation ◽  
Periodic Functions ◽  
Exact Bounds

Certain exact bounds for seminorms given on spaces of periodic functions

1977 ◽  
Vol 21 (6) ◽  
pp. 445-450
Author(s):  
V. V. Zhuk
Keyword(s):  
Periodic Functions ◽  
Exact Bounds

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.

Exact bounds for norms of differentiable periodic functions in L metric

1967 ◽  
Vol 2 (6) ◽  
pp. 839-843 ◽  
Author(s):  
N. P. Korneichuk
Keyword(s):  
Periodic Functions ◽  
Exact Bounds

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.

A Study of Uniform Approximation of Plane Gratings by Oblique Incidence

2008 ◽  
Vol 128 (9) ◽  
pp. 598-599 ◽  
Author(s):  
Hideaki Wakabayashi ◽  
Jiro Yamakita
Keyword(s):  
Uniform Approximation ◽  
Oblique Incidence

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.

Sign in / Sign up

Export Citation Format

Share Document