Abstract
In this paper, we generalized the results of [23, 26], and get the results of the condition number of the W-weighted Drazin-inverse solution of linear system W AWx = 6, where A is an m × n rank-deficient matrix and the index of AW is k<sub>1</sub>, the index of W A is k<sub>2</sub>, b is a real vector of size n in the range of (W A)<sup>k2</sup>, x is a real vector of size m in the range of (AW)<sup>k1</sup>. Let α and β be two positive real numbers, when we consider the weighted Frobenius norm ∥ [αW AW, βb] ∥<sub>Q,P̄</sub><sup>(F)</sup>. on the data we get the formula of condition number of the W-weighted Drazin-inverse solution of linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated. © 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.
| Original language | English |
|---|---|
| Pages (from-to) | 35-59 |
| Journal | Journal of Applied Mathematics and Computing |
| Volume | 20 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - Jan 2006 |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- Componentwise perturbation
- Condition number
- Linear system
- W-weighted Drazin inverse
- W-weighted Drazininverse solution
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