New Methods for Localizing Discontinuities of a Noisy Function

被引：6

作者：

Antonova, T. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Math & Mech, Ural Branch, Ul S Kovalevskoi 16, Ekaterinburg 620990, Russia

来源：

NUMERICAL ANALYSIS AND APPLICATIONS | 2010年 / 3卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

ill-posed problems; localization of singularities; discontinuities of the first kind; regularizing method; separability threshold;

D O I：

10.1134/S1995423910040026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a problem of localizing singularities (discontinuities of the first kind) of a noisy function in L-p (1 <= p < infinity), new classes of regularizing methods are constructed. The methods determine the number of discontinuities and approximate their positions. The upper and lower bounds of the localizing singularities and the separability threshold are also obtained. It is proved that the methods are order-optimal by accuracy and separability on some classes of functions with discontinuities.

引用

页码：306 / 316

页数：11

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