Mixed,componentwise condition numbers and small sample statistical condition estimation of Sylvester equations |
| |
| Authors: | Huaian Diao Hua Xiang Yimin Wei |
| |
| Institution: | 1. School of Mathematics and Statistics, Northeast Normal University, , Chang Chun, 130024 China;2. School of Mathematics and Statistics, Wuhan University, , Wuhan, 430072 China;3. School of Mathematical Sciences, Fudan University, , Shanghai, 200433 China;4. Shanghai Key Laboratory of Contemporary Applied Mathematics, , Shanghai, 200433 China |
| |
| Abstract: | We present a componentwise perturbation analysis for the continuous‐time Sylvester equations. Componentwise, mixed condition numbers and new perturbation bounds are derived for the matrix equations. The small sample statistical method can also be applied for the condition estimation. These condition numbers and perturbation bounds are tested on numerical examples and compared with the normwise condition number. The numerical examples illustrate that the mixed condition number gives sharper bounds than the normwise one. Copyright © 2011 John Wiley & Sons, Ltd. |
| |
| Keywords: | Sylvester equations condition number componentwise perturbation small sample statistical method |
|
|
