A note on condition numbers for generalized inverse AT,S-(2) and constrained linear systems

作者：Liu, Gang; Lu, Shengqi; Chen, Juping; Xu, Wei^*

来源：Applied Mathematics and Computation, 2010, 217(7): 3199-3206.

DOI：10.1016/j.amc.2010.08.052

• Condition number
• Perturbation
• Generalized inverse A(T,S)((2))
• Schur decomposition
• Index

In this paper, we use the Schur decomposition to measure the sensitivity of the general inverse A(T,S)((2)) and the constrained singular linear system Ax = b with regard to 2-norm and F-norm, rather than PQ-norm in [12], where P and Q are nonsingular matrices. The explicit forms of the condition numbers approximate the sensitivity of A(T,S)((2)) and the constrained singular linear system pretty well. Furthermore, since Schur decomposition is well-posed, the evaluation of the sensitivity can be numerically easy and stable.

• 出版日期2010-12-1
• 单位复旦大学; 同济大学