Uniform approximation of multidimensional myopic maps

Sandberg I.W.; Xu L.

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Uniform approximation of multidimensional myopic maps

机译：多维近视图的均匀逼近

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摘要

Our main result is a theorem that gives, in a certain setting, a necessary and sufficient condition under which multidimensional shift-invariant input-output maps with vector-valued inputs drawn from a certain large set can be uniformly approximated arbitrarily well using a structure consisting of a linear preprocessing stage followed by a memoryless nonlinear network. Noncausal as well as causal maps are considered. Approximations for noncausal maps for which inputs and outputs are functions of more than one variable are of current interest in connection with, for example, image processing

机译：我们的主要结果是得出一个定理，该定理给出了一个必要的充分条件，在该条件下，具有以下条件的多维平移不变输入输出映射具有从某个大集合中提取的向量值输入，就可以使用线性预处理阶段，然后是无记忆非线性网络。考虑非因果图和因果图。对于非因果图，其输入和输出是一个以上变量的函数的近似值，例如与图像处理有关，目前受到关注

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《IEEE Transactions on Circuits and Systems. I, Regular Papers》 |1997年第6期|p.477-500|共24页
作者
Sandberg I.W.; Xu L.;
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原文格式 PDF
正文语种 eng
中图分类 TN71;
关键词
approximation theory; memoryless systems; multidimensional systems; nonlinear systems; causal map; image processing; linear preprocessing; memoryless nonlinear network; multidimensional myopic map; noncausal map; shift-invariant input-output map; uniform approximat;

机译：近似理论;无记忆系统;多维系统;非线性系统;因果图;图像处理;线性预处理;无记忆非线性网络;多维近视图;无因果图;不变变量输入输出图;均匀近似;

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专利

1. Uniform approximation of multidimensional myopic maps [J] . Sandberg I.W., Xu L. IEEE Transactions on Circuits and Systems. 1 . 1997,第6期

机译：多维近视图的均匀逼近
2. Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps [J] . Bahsoun Wael, Bose Christopher, Duan Yuejiao Ergodic Theory and Dynamical Systems . 2015,第Pta4期

机译：非均匀扩展图不变密度的严格逐点逼近
3. Stability and Approximation of Statistical Limit Laws for Multidimensional Piecewise Expanding Maps [J] . Crimmins Harry, Froyland Gary Annales Henri Poincare . 2019,第9期

机译：多维分段扩展地图统计限制法的稳定性和近似
4. Separation conditions and criteria for uniform approximation of input-output maps [C] . Sandberg, I.W. . 1998

机译：输入输出映射的统一逼近的分离条件和准则
5. Flux maps obtained from core geometry approximations: Monte Carlo simulations and benchmark measurements for a 250 kw TRIGA reactor [D] . Mohamed, Ali Bellou. 2009

机译：从堆芯几何近似值获得的通量图：250 kW TRIGA反应堆的蒙特卡洛模拟和基准测量
6. Analysis and implications of equivalent uniform approximations of nonuniform unitary synaptic systems. [O] . V V Uteshev, J B Patlak, P S Pennefather 2000

机译：非均匀unit突触系统的等效均匀逼近的分析和含义。
7. Semiclassical collision theory. Application of multidimensional uniform approximations to the atom-rigid-rotor system [O] . Kreek H., Ellis R. L., Marcus R. A. 1975

机译：半经典碰撞理论。多维均匀逼近在原子刚性转子系统中的应用
8. Mean Power, Uniform (Chebyshevskiy) and Quasi-Uniform Approximations. [R] . Remez, Y. Y. 1977

机译：平均功率，均匀（Chebyshevskiy）和拟均匀近似。

Uniform approximation of multidimensional myopic maps

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