Minimax State Estimates for Abstract Neumann Problems

Sergiy Zhuk; Olexander Nakonechnii

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Minimax State Estimates for Abstract Neumann Problems

机译：极小极大状态估计抽象诺伊曼问题

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摘要

The paper presents analytic expressions of minimax (worst-case) estimates for solutions of linear abstract Neumann problems in Hilbert space with uncertain (not necessarily bounded!) inputs and boundary conditions given incomplete observations with stochastic noise. The latter is assumed to have uncertain but bounded correlation operator. It is demonstrated that the minimax estimate is asymptotically exact under mild assumptions on the observation operator and the bounding sets. A relationship between the proposed estimates and a robust pseudo-inversion of compact operators is revealed. This relationship is demonstrated on an academic numerical example: homogeneous Neumann problem for Poisson equation in two spatial dimensions.

机译：提出了极大极小的解析表达式(坏的)估计的线性的解决方案抽象的诺伊曼在希尔伯特空间问题不确定(不一定有界!)输入和边界条件给定的不完整的观察与随机噪声。不确定但有界相关算子。这是证明了极大极小估计是渐近准确下温和的假设观察操作符和边界集。建议预算和之间的关系健壮的pseudo-inversion紧凑的运营商透露。学术数值例子:齐次纽曼泊松方程在两个空间的问题维度。

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《Minimax theory and its applications》 |2018年第1期|1-21|共21页
作者
Sergiy Zhuk; Olexander Nakonechnii;
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作者单位

T. Shevchenko University of Kyiv, Kyiv, Ukraine;

IBM Research, Dublin, Ireland;

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原文格式 PDF
正文语种英语
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关键词
Minimax; Neumann problem; Filtrationcorrelation operatorUncertaintyPoisson equationlinear operators;

机译：极大极小,诺伊曼问题;FiltrationcorrelationoperatorUncertaintyPoisson equationlinear运营商;

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Minimax State Estimates for Abstract Neumann Problems

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