收稿日期: 2004-03-03
网络出版日期: 2005-01-15
基金资助
国家科技部“国家重点实验室网上合作研究平台”项目 (2003DEA5G040);中国科学院研究生院院长基金项目 (YZJJ200206)资助
Transductive Inference Based Multi Dimensional Neville Algorithm for Estimating Values of Functions
Received date: 2004-03-03
Online published: 2005-01-15
根据转导思想的函数估计，不用估计函数的模型和参数，直接估计函数在给定点的值，从根本上区别于传统的函数估计方法，但具体的实现算法是一个公开的问题。讨论使用多维Neville算法实现基于转导思想的函数估计的问题。利用投影的方法，将传统的Neville算法推广到了多维空间，在数值计算中引入了核函数的思想，从而解决了多维空间的计算问题，得到利用多维的Neville算法实现函数估计的方法。数值试验的结果表明，这种方法成功地克服了函数插值的龙格 (Runge)现象，有很好的逼近效果，并且可以处理多维的函数估计问题 ;同时也给出了对核函数参数进行估计这个难题的一些讨论。该算法对转导思想的实现提供了一个崭新的途径。
马琳 , 叶世伟 , 罗铁坚 , 宋进亮 . 利用多维Neville算法实现基于转导思想的函数估计[J]. 中国科学院大学学报, 2005 , 22(1) : 64 -71 . DOI: 10.7523/j.issn.2095-6134.2005.1.010
An algorithm based on transductive inference learning used for estimating values of functions .It does not use any predefined modules and parameters and estimates the values of functions directly .It is the biggest difference between traditional algorithms for estimating values of functions .But the most trouble is how to implement the algorithm.Our paper discusses a transductive inference based multi dimensional Neville algorithm for estimating values of functions .By the use of projecting methods , we get multi dimensional Neville algorithm for estimating values of functions .The results of experiments show our algorithm not only successfully overcomes Runge problem of traditional algorithm for estimating values of functions , but also has a very nice function values estimating results and can be used in multi dimensional circumstance .We also provide some discussion of the selection of kernel parameters .Our algorithm shows a brand new way in transductive inference field .
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