RUI: Applications of Approximation Theory to Neural Networks and Wavelets

RUI：近似理论在神经网络和小波中的应用

• 批准号: 9971846
• 负责人: Hrushikesh Mhaskar
• 金额: $ 12万
• 依托单位: California State University-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2003-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971846&HistoricalAwards=false
• 关键词: RUI; Applications; Approximation; Theory; Neural

Mhaskar will continue his investigations on the complexity problem inthe theory of neural networks and construction of multiscales based onorthogonal polynomial coefficients as well as samples of the targetfunctions. Variations of such classical methods from approximationtheory as summability methods and polynomial inequalities will bedeveloped to provide a unified theory of these apparently diverse areas.The work will be applied to the numerical construction of orthogonalpolynomials, approximation on the sphere using scattered data, and thetheory of system identification.Although approximation theory is a classical area of mathematics, activefor more than a hundred years, technological progress in the areas ofneural networks and wavelets has given rise to many new possibilitiesfor applications of approximation theory. Neural networks and waveletsare both useful in high speed parallel computing, and naturally involvethe approximation of functions. Approximation theory techniques usedwith neural networks have produced dramatically better results incertain applications to array antenna technology, pattern recognition,and financial time series prediction.

Mhaskar将继续他的调查复杂性问题的理论神经网络和建设多尺度的基础上正交多项式系数以及样本的目标功能。近似理论的经典方法的变体，如求和方法和多项式不等式，将被发展为这些明显不同的领域提供一个统一的理论。这项工作将被应用于正交多项式的数值构造，使用离散数据的球面近似，以及系统识别理论。虽然近似理论是数学的经典领域，活跃了一百多年，神经网络和小波领域的技术进步为逼近理论的应用带来了许多新的可能性。神经网络和小波都适用于高速并行计算，并且自然涉及函数的逼近。近似理论技术与神经网络一起使用，在阵列天线技术、模式识别和金融时间序列预测的某些应用中产生了明显更好的结果。