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首页> 外文期刊>Journal of applied and industrial mathematics >Approximation of discontinuity lines for a noisy function of two variables with countably many singularities
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Approximation of discontinuity lines for a noisy function of two variables with countably many singularities

机译：具有奇异数的两个变量的噪声函数的不连续线的逼近

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摘要

We construct and study the methods of localization (positioning) of the lines in whose neighborhoods a measured function of two variables is smooth, whereas at each point of the lines it has discontinuity of the first kind (i.e., lines of discontinuity). Assume that the function has countably many discontinuity lines: on finitely many of them the function has a "large" jump, whereas the jump values on the other lines satisfy some smallness condition. Given a noise-contaminated function and an error level in L 2, it is required to determine the number and localize the position of discontinuity lines from the first set for the exact function. This problem belongs to the class of nonlinear ill-posed problems and, to solve it, we need to construct some regularizing algorithms. Some simplified theoretical approach is proposed in the case when the conditions on the exact function are imposed in a narrow strip intersecting the discontinuity lines.We constructed the averaging methods and obtained accuracy estimates for the localization of discontinuity lines.
机译：我们构建并研究了在其邻域中两个变量的测量函数很平滑的线的定位（定位）方法，而在线的每个点上都具有第一类不连续性（即不连续的线）。假设函数具有许多不连续线：在有限的许多不连续线上，函数具有“大”跳转，而其他行上的跳转值满足某些较小性条件。给定一个受噪声污染的函数，误差水平为L 2，则需要确定数量并从不连续线的位置开始定位确切函数的不连续线。该问题属于非线性不适定问题的类别，要解决该问题，我们需要构造一些正则化算法。当在不连续线相交的窄条上施加精确函数的条件时，提出了一些简化的理论方法。我们构造了求平均值的方法，并获得了不连续线定位的精度估计。

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