On discretization of methods for localization of singularities a noisy function

被引：0

作者：

Ageev, A. L. ^{[1
,2
]}

Antonova, T. V. ^{[3
,4
]}

机构：

[1] Russian Acad Sci, Inst Math & Mech, Ural Branch, Phys Mat Sci, Moscow, Russia

[2] Russian Acad Sci, Inst Math & Mech, Ural Branch, Moscow, Russia

[3] Ural Fed Univ, Phys Mat Sci, Ekaterinburg, Russia

[4] Ural Fed Univ, Ekaterinburg, Russia

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2015年 / 21卷 / 01期

关键词：

ill-posed problem; discontinuity of the first kind; localization of singularities; regularizing method; discretization;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Ill-posed problems of localizing the singularities of a noisy function of one or two variables are studied. For functions of one variable, singularities are discontinuities of the first kind; for a function of two variables, singularities are lines of discontinuity. The discretization of regular localization methods is investigated. Correctness classes are introduced, and error estimates are obtained for the approximation of singularities and separability threshold of the constructed algorithms. It is shown that discrete algorithms for localizing discontinuities of the first kind of a noisy function of one variable are order-optimal.

引用

页码：3 / 13

页数：11

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