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利用Gaussian核对多元函数的近似逼近及其误差估计
  • ISSN号：1001-8395
  • 期刊名称：《四川师范大学学报：自然科学版》
  • 时间：0
  • 分类：O174.41[理学—数学;理学—基础数学]
  • 作者机构：[1]西华大学数学与计算机学院,四川成都610039
  • 相关基金：国家自然科学基金（10671019）; 教育部博士点基金（20050027007）; 四川省科技厅重点项目基金（05JY029-138）资助项目
作者： 徐艳艳[1], 陈广贵[1], 雷文慧[1]
关键词： Gaussian核, 近似逼近数, 全误差, TAYLOR公式, Gaussian kernel, Approximate approximation, Total error, Taylor’s formula
中文摘要：

V.Maz’ya首次提出了近似逼近法,其主要是研究定义在全空间上的光滑函数的逼近情况,但它不能有效的处理积分和拟微分算子的高阶求积公式问题及利用更有效的数值和半数值方法解决数学物理的边界等问题.F.M櫣ller和W.Varnhorn给出了一维紧区间上函数的近似逼近方法,而且还可以控制近似逼近的截断误差.根据上述思想,采用近似逼近法,利用Gaussian核对二维紧空间上光滑函数进行逼近,并考察由这种近似逼近法所产生的误差情况.

英文摘要：

Maz’ya introduced a method of approximate approximations which had mainly been used for functions defined on the whole space. However,it was difficult for this method to treat the differential equations and boundary integral equations. Then,F. Müller and W. Varnhorn applied the method of approximate approximation to functions which are defined on compact intervals and investigated the error. In this paper,we study approximate approximation with Gaussian kernels on multivariate compact intervals as well as the error estimates.

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期刊信息
  • 《四川师范大学学报：自然科学版》
  • 中国科技核心期刊
  • 主管单位:四川省教育厅
  • 主办单位:四川师范大学
  • 主编：王学平
  • 地址：成都市锦江区静安路5号
  • 邮编：610066
  • 邮箱：
  • 电话：028-84760704
  • 国际标准刊号：ISSN：1001-8395
  • 国内统一刊号：ISSN：51-1295/N
  • 邮发代号:
  • 获奖情况:
  • 2009年获“中国科技论文在线优秀期刊”二等奖,2010年获教育部科学技术司第三届“中国高校优秀科...,2010年“四川省科技期刊精品期刊”,2011年中国高校科技期刊研究会“十佳学报”,2011年“2011年度中国精品科技期刊”
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国化学文摘（网络版）,美国数学评论（网络版）,德国数学文摘,英国动物学记录,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:7680