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True Condition Number

For linear system Ax = b, the traditional condition number is the worst case for all
b¡¦s and often overestimated in many problems. For a specific b, the effective condition
number is a better upper bound for the relative error of x. But, it is also possible
that this effective condition number is overestimated. In this thesis, we study the true
ratio of the relative error of x to the relative perturbation of b, called the true condition
number. We obtain several new upper bounds and estimates for true condition
number. We also explore to change the system to an equivalent one by shifting b to
minimize its effective condition number. Finally we apply all our results to functional
approximation.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0814111-210902
Date14 August 2011
CreatorsLin, Tzu-Yuan
ContributorsTzon-Tzer Lu, Chien-Sen Huang, Hung-Tsai Huang, Tsung-Lin Lee, Zi-Cai Li
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0814111-210902
Rightsuser_define, Copyright information available at source archive

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