Results 1 to 10 of about 1,637,948 (328)

On Rate of Approximation by Modified Beta Operators [PDF]

International Journal of Mathematics and Mathematical Sciences, 2009
We establish the rate of convergence for the modified Beta operators 𝐵𝑛(𝑓,𝑥), for functions having derivatives of bounded variation.
Prerna Maheshwari (Sharma), Vijay Gupta
doaj   +4 more sources

Convergence rate of linear two-time-scale stochastic approximation [PDF]

, 2004
We study the rate of convergence of linear two-time-scale stochastic approximation methods. We consider two-time-scale linear iterations driven by i.i.d. noise, prove some results on their asymptotic covariance and establish asymptotic normality.
Konda, Vijay R., Tsitsiklis, John N.
core   +2 more sources

Equivalence of rate of approximation and smoothness

Journal of Approximation Theory, 1990
The result of Jackson and Bernstein \[ \omega^ r(f,t)=O(t^{\alpha})\Leftrightarrow E_ n(f)=O(n^{-\alpha}) \] have led to the question whether \(\omega^ r(f,\frac{1}{n})\sim E_ n(f)?\) The answer is affirmative, if the function \(\psi_ r(t):=\omega^ r(f,t)\) satisfies \[ \delta^ r\int^{c}\frac{\psi_ r(t)}{t^{r+1}}dt\sim \psi_ r(\delta). \] The analogous
Z. Ditzian
openaire   +2 more sources

About the rate of rational approximation of some analytic functions

Mathematical Modelling and Analysis, 1998
The article is devoted to results relating to the theory of rational approximation of an analytic function. Let ƒ be an analytic function on the disk {z : |z| < ñ), ñ > 1. The rate of decrease of the best approximations ñn of a function ƒ by the rational
A. YA. Radyno
doaj   +5 more sources

Approximation by matrix transform in generalized grand Lebesgue spaces with variable exponent

Journal of Numerical Analysis and Approximation Theory, 2021
In this work the Lipschitz subclass of the generalized grand Lebesgue space with variable exponent is defined and the error of approximation by matrix transforms in this subclass is estimated.
Ahmet Testici, Daniyal Israfilov
doaj   +7 more sources

Optimal Approximation Rate of ReLU Networks in terms of Width and Depth [PDF]

Journal des Mathématiques Pures et Appliquées, 2021
This paper concentrates on the approximation power of deep feed-forward neural networks in terms of width and depth. It is proved by construction that ReLU networks with width O ( max ⁡ { d ⌊ N 1 / d ⌋ , N + 2 } ) and depth O ( L ) can approximate a ...
Zuowei Shen, Haizhao Yang, Shijun Zhang
semanticscholar   +1 more source

Rate of convergence for particle approximation of PDEs in Wasserstein space [PDF]

Journal of Applied Probability, 2021
We prove a rate of convergence for the N-particle approximation of a second-order partial differential equation in the space of probability measures, such as the master equation or Bellman equation of the mean-field control problem under common noise ...
Maximilien Germain, H. Pham, X. Warin
semanticscholar   +1 more source

Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series; pp 50-60 [PDF]

Proceedings of the Estonian Academy of Sciences, 2018
We extend the results presented by Xh. Z. Krasniqi (Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of Lp. Acta Comment. Univ. Tartu. Math., 2013, 17, 89–101) and W. Lenski and B.
Włodzimierz Łenski, Bogdan Szal
doaj   +1 more source

Minimum rates of approximate sufficient statistics [PDF]

2017 IEEE International Symposium on Information Theory (ISIT), 2017
Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, for $n$ independent samples drawn from a $k$-nomial distribution with $d=k-1$ degrees of freedom, the length
Masahito Hayashi, Vincent Y. F. Tan
openaire   +2 more sources

On Lagrange polynomials and the rate of approximation of planar sets by polynomial Julia sets [PDF]

Journal of Mathematical Analysis and Applications, 2017
We revisit the approximation of nonempty compact planar sets by filled-in Julia sets of polynomials developed in [27] and analyze the rate of approximation.
L. Białas-Cież, M. Kosek, Małgorzata Stawiska   +2 more
semanticscholar   +1 more source