区间分析的基本定理

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI:10.1109/scan.2006.43

M. H. Emden, B. Moa

{"title":"区间分析的基本定理","authors":"M. H. Emden, B. Moa","doi":"10.1109/scan.2006.43","DOIUrl":null,"url":null,"abstract":"Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"80 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Fundamental Theorems of Interval Analysis\",\"authors\":\"M. H. Emden, B. Moa\",\"doi\":\"10.1109/scan.2006.43\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis.\",\"PeriodicalId\":388600,\"journal\":{\"name\":\"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)\",\"volume\":\"80 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/scan.2006.43\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/scan.2006.43","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

表达式不是函数。混淆这两个概念或不能定义由表达式计算的函数会削弱区间算术的严谨性。我们给出了这样一个定义，并继续对区间算术和区间分析的基本定理进行了必要的重述和证明。

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

The Fundamental Theorems of Interval Analysis

Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis.

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

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)

自引率

0.00%

发文量