一般三次hermite - pad近似的存在性及局部性质

2010 Second International Conference on Computational Intelligence and Natural Computing Pub Date : 2010-11-22 DOI:10.1109/CINC.2010.5643818

Li Jin

{"title":"一般三次hermite - pad<s:1>近似的存在性及局部性质","authors":"Li Jin","doi":"10.1109/CINC.2010.5643818","DOIUrl":null,"url":null,"abstract":"This paper analyses the local behavior of the general cubic function approximation to a function which has a given power series expansion about the origin. It is shown that the general cubic Hermite-Padé form always defines a cubic function and that this function is analytic in a neighbourhood of the origin. This result holds even if the origin is a critical point of the function (i.e., the discriminant has a zero at the origin).","PeriodicalId":227004,"journal":{"name":"2010 Second International Conference on Computational Intelligence and Natural Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and local behavior of general cubic Hermite-Padé Approximation\",\"authors\":\"Li Jin\",\"doi\":\"10.1109/CINC.2010.5643818\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper analyses the local behavior of the general cubic function approximation to a function which has a given power series expansion about the origin. It is shown that the general cubic Hermite-Padé form always defines a cubic function and that this function is analytic in a neighbourhood of the origin. This result holds even if the origin is a critical point of the function (i.e., the discriminant has a zero at the origin).\",\"PeriodicalId\":227004,\"journal\":{\"name\":\"2010 Second International Conference on Computational Intelligence and Natural Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 Second International Conference on Computational Intelligence and Natural Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CINC.2010.5643818\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Second International Conference on Computational Intelligence and Natural Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CINC.2010.5643818","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文分析了一般三次函数逼近在原点上具有给定幂级数展开式的函数的局部性质。证明了一般三次hermite - pad形式总是定义一个三次函数，并且该函数在原点的邻域中是解析的。即使原点是函数的临界点(即，判别式在原点处为零)，这个结果也成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Existence and local behavior of general cubic Hermite-Padé Approximation

This paper analyses the local behavior of the general cubic function approximation to a function which has a given power series expansion about the origin. It is shown that the general cubic Hermite-Padé form always defines a cubic function and that this function is analytic in a neighbourhood of the origin. This result holds even if the origin is a critical point of the function (i.e., the discriminant has a zero at the origin).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

2010 Second International Conference on Computational Intelligence and Natural Computing

自引率

0.00%

发文量