On the Localization of Fractal Lines of Discontinuity from Noisy Data

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2023-09-01 DOI:10.3103/s1066369x23090037

引用次数: 0

Abstract

An ill-posed problem of localization (determining the position) of discontinuity lines of a function of two variables is considered: outside the discontinuity lines, the function is smooth, and, at each point on the line, it has a discontinuity of the first kind. Under the Lipschitz conditions on the discontinuity line, averaging procedures are constructed and global discrete regularizing algorithms of localization are studied. A parametric family of fractal lines is constructed for which all conditions can be checked analytically. A fractal having a large fractal dimension is indicated for which the efficiency of the constructed methods can be guaranteed.

查看原文本刊更多论文

论从噪声数据中定位分形不连续线

摘要研究了双变量函数不连续线的定位（确定位置）问题：在不连续线外，函数是光滑的，在不连续线上的每一点，函数都有第一类不连续。在不连续线的 Lipschitz 条件下，构建了平均程序，并研究了局部化的全局离散正则化算法。构建了分形线的参数族，对其所有条件都可以进行分析检验。还指出了一种具有较大分形维度的分形，对于这种分形，所构建方法的效率可以得到保证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.