Optimization of active algorithms for recovery of monotonic functions from Hölder's class
type: Item
instance of: scholarly article
title: Optimization of active algorithms for recovery of monotonic functions from Hölder's class
zbMATH Open document ID: 0807.65006
author: N. P. Korneichuk
published in: Journal of Complexity
publication date: 1994-10-17T00:00:00Z
review text: Let \(H^ \alpha\) be the class of all functions \(f\in C([a,b])\) satisfying for \(0< \alpha\leq 1\) the condition \(| f(x')- f(x'')|\leq | x'- x''|^ \alpha\), \(x',x''\in [a,b]\) and let \(H^ \alpha_ m\) be the set of monotonic functions in \(H^ \alpha\). The relationship of passive and active algorithms in problems of recovery of functions is considered. The author proves that bisection is optimal among all active algorithms in the problem of recovery of functions \(f\in H^ \alpha_ m\) with metric \(C\) and when \(0< \alpha<1\) it achieves the best order \(O(N^{- 1}\log_ 2 N)\) on the set \(H^ \alpha_ m\).
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 638541
zbMATH Keywords: recovery of monotonic functions
zbMATH Keywords: Hölder's class
zbMATH Keywords: active algorithms
zbMATH Keywords: bisection
MaRDI profile type: Publication
full work available at URL: jcom.1994.1013
OpenAlex ID: W2025324891
DOI: 10.1006/JCOM.1994.1013
description: scientific article; zbMATH DE number 638541