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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0814111-210902 |
| Date | 14 August 2011 |
| Creators | Lin, Tzu-Yuan |
| Contributors | Tzon-Tzer Lu, Chien-Sen Huang, Hung-Tsai Huang, Tsung-Lin Lee, Zi-Cai Li |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0814111-210902 |
| Rights | user_define, Copyright information available at source archive |
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