A note on homotopic backward error and pseudospectra for the generalized eigenproblem Ax =.pdfVIP

下载本文档

6
0
约8.16千字
约 5页
2017-04-11 发布于江苏
举报
版权申诉

A note on homotopic backward error and pseudospectra for the generalized eigenproblem Ax =.pdf

1、有哪些信誉好的足球投注网站（book118）网站文档一经付费（服务费），不意味着购买了该文档的版权，仅供个人/单位学习、研究之用，不得用于商业用途，未经授权，严禁复制、发行、汇编、翻译或者网络传播等，侵权必究。。
2、本站所有内容均由合作方或网友上传，本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺！文档内容仅供研究参考，付费前请自行鉴别。如您付费，意味着您自己接受本站规则且自行承担风险，本站不退款、不进行额外附加服务；查看《如何避免下载的几个坑》。如果您已付费下载过本站文档，您可以点击这里二次下载。
3、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等，请点击“版权申诉”（推荐），也可以打举报电话：400-050-0827(电话支持时间：9:00-18:30)。
4、该文档为VIP文档，如果想要下载，成为VIP会员后，下载免费。
5、成为VIP后，下载本文档将扣除1次下载权益。下载后，不支持退款、换文档。如有疑问请联系我们。
6、成为VIP后，您将拥有八大权益，权益包括：VIP文档下载权益、阅读免打扰、文档格式转换、高级专利检索、专属身份标志、高级客服、多端互通、版权登记。
7、VIP文档为合作方或网友上传，每下载1次，网站将根据用户上传文档的质量评分、类型等，对文档贡献者给予高额补贴、流量扶持。如果你也想贡献VIP文档。上传文档

A note on homotopic backward error and pseudospectra for the generalized eigenproblem Ax =

A note on homotopic backward error and pseudospectra forthe generalized eigenproblem Ax = BxV. Toumazou E. Traviesas yCERFACS Technical Report TR/PA/99/14 - April 1999AbstractWe present the notion of backward error and pseudospectra for homotopic pertur-bations in the case of the generalized eigenproblem Ax = Bx. This is an extensionof the notions introduced in [2] for the standard problem.1 IntroductionIn order to assess the validity of an approximate solution (computed exactly) or acomputed solution (in nite precision), one can use the notion of backward error. Asit was fully described in [2] for the standard problem, in stability analysis, one has todene the data to be perturbed, the type of the perturbations to be considered andthe metrics to measure data and perturbations. The cases of normwise and homotopicperturbations were compared in [2] for the standard problem.For the generalized eigenproblem Ax = Bx, the notion of normwise backward errorhas been studied in [4] and we introduce, in this note, the notions of homotopic back-ward error and pseudospectra.The problem Ax = Bx or equivalently the matrix pair (A;B) is said to be regularif there exists at least one complex number z for which det(A zB) 6= 0. Otherwiseit is said singular. When B is nonsingular, regular matrix pairs (A;B) have the samespectrum as B1A. When B is singular, the matrix pair admits at least one inniteeigenvalue.In this paper, we restrict our study to regular matrix pairs. Therefore, we can ensurethat all the eigenvalues of the matrix pair (A;B) are nite.2 Backward analysis for homotopic perturbationsLet us consider A and B homotopic perturbations of A and BA = tE and B = tFC.E.R.F.A.C.S, 42, avenue G. Coriolis 31057 Toulouse cedex, toumazou@cerfacs.fryUniversite des Sciences Sociales, Toulouse 1 and C.E.R.F.A.C.S, 42, avenue G. Coriolis 31057 Toulousecedex,travies@cerfacs.fr 1 2 BACKWARD ANALYSIS FOR HOMOTOPIC PERTURBATIONS 2where E and F are given deviation matrices