近似Gröbner基的理论与算法

2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Pub Date : 2011-09-26 DOI:10.1109/SYNASC.2011.12

Tateaki Sasaki

{"title":"近似Gröbner基的理论与算法","authors":"Tateaki Sasaki","doi":"10.1109/SYNASC.2011.12","DOIUrl":null,"url":null,"abstract":"In this paper, we treat polynomials with coefficients of floating-point numbers. The conventional concept of ideal breaks down for such polynomials, and we first define a concept of \"approximate ideal''. Then, introducing \"accuracy-guarding reductions'', we define approximate Groebner bases and give an algorithm for computing the approximate Groebner bases. We prove several theorems showing basic properties of approximate Groebner bases. The algorithm has been implemented, and we explain the approximate Groebner bases concretely by instructive examples.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"A Theory and an Algorithm of Approximate Gröbner Bases\",\"authors\":\"Tateaki Sasaki\",\"doi\":\"10.1109/SYNASC.2011.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we treat polynomials with coefficients of floating-point numbers. The conventional concept of ideal breaks down for such polynomials, and we first define a concept of \\\"approximate ideal''. Then, introducing \\\"accuracy-guarding reductions'', we define approximate Groebner bases and give an algorithm for computing the approximate Groebner bases. We prove several theorems showing basic properties of approximate Groebner bases. The algorithm has been implemented, and we explain the approximate Groebner bases concretely by instructive examples.\",\"PeriodicalId\":184344,\"journal\":{\"name\":\"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"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.2011.12\",\"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.2011.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 9

摘要

在本文中，我们处理系数为浮点数的多项式。对于这类多项式，传统的理想概念被打破了，我们首先定义了“近似理想”的概念。然后，引入“精度保护约简”，定义近似Groebner基，并给出近似Groebner基的计算算法。我们证明了几个定理，证明了近似格罗布纳基的基本性质。该算法已实现，并通过实例具体说明了近似格罗布纳基。

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

A Theory and an Algorithm of Approximate Gröbner Bases

In this paper, we treat polynomials with coefficients of floating-point numbers. The conventional concept of ideal breaks down for such polynomials, and we first define a concept of "approximate ideal''. Then, introducing "accuracy-guarding reductions'', we define approximate Groebner bases and give an algorithm for computing the approximate Groebner bases. We prove several theorems showing basic properties of approximate Groebner bases. The algorithm has been implemented, and we explain the approximate Groebner bases concretely by instructive examples.

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