验证了无限维特征值问题的计算

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-12-01 DOI:10.1109/SCAN.2006.48

K. Nagatou

{"title":"验证了无限维特征值问题的计算","authors":"K. Nagatou","doi":"10.1109/SCAN.2006.48","DOIUrl":null,"url":null,"abstract":"In this paper we will show how guaranteed bounds for eigenvalues (together with eigenvectors) are obtained and how non-existence of eigenvalues in a concrete region could be assured. Some examples for several types of operators in bounded and unbounded domains will be presented. We will furthermore discuss possible future applications to eigenvalue enclosing/excluding of Schrodinger operator, hopefully in its spectral gaps.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"447 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Validated computation for infinite dimensional eigenvalue problems\",\"authors\":\"K. Nagatou\",\"doi\":\"10.1109/SCAN.2006.48\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we will show how guaranteed bounds for eigenvalues (together with eigenvectors) are obtained and how non-existence of eigenvalues in a concrete region could be assured. Some examples for several types of operators in bounded and unbounded domains will be presented. We will furthermore discuss possible future applications to eigenvalue enclosing/excluding of Schrodinger operator, hopefully in its spectral gaps.\",\"PeriodicalId\":388600,\"journal\":{\"name\":\"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)\",\"volume\":\"447 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"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.2006.48\",\"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.2006.48","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 6

摘要

在本文中，我们将证明如何获得特征值(连同特征向量)的保证界，以及如何保证特征值在一个具体区域内不存在。给出了有界和无界域中几种类型算子的一些例子。我们将进一步讨论薛定谔算子的特征值封闭/排除可能的未来应用，希望在其谱间隙中。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Validated computation for infinite dimensional eigenvalue problems

In this paper we will show how guaranteed bounds for eigenvalues (together with eigenvectors) are obtained and how non-existence of eigenvalues in a concrete region could be assured. Some examples for several types of operators in bounded and unbounded domains will be presented. We will furthermore discuss possible future applications to eigenvalue enclosing/excluding of Schrodinger operator, hopefully in its spectral gaps.

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