论Kahan确定分支切割的规则

2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Pub Date : 2011-09-13 DOI:10.1109/SYNASC.2011.51

F. Chyzak, J. Davenport, C. Koutschan, B. Salvy

{"title":"论Kahan确定分支切割的规则","authors":"F. Chyzak, J. Davenport, C. Koutschan, B. Salvy","doi":"10.1109/SYNASC.2011.51","DOIUrl":null,"url":null,"abstract":"In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"74 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On Kahan's Rules for Determining Branch Cuts\",\"authors\":\"F. Chyzak, J. Davenport, C. Koutschan, B. Salvy\",\"doi\":\"10.1109/SYNASC.2011.51\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.\",\"PeriodicalId\":184344,\"journal\":{\"name\":\"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"volume\":\"74 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2011.51\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2011.51","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

在计算机代数中，有不同的方法来接近函数的数学概念，其中一种方法是将它们定义为微分方程的解。我们比较了不同的方法，并讨论了出现的问题。主要焦点是确定可能的分支削减问题。我们通过将Kahan的规则适应于微分方程设置，探索分支切割的处理可以呈现(更多)算法的程度。

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

On Kahan's Rules for Determining Branch Cuts

In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.

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

2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

自引率

0.00%

发文量