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

摘要

In this paper, we use the Schur decomposition to measure the sensitivity of the general inverse AT,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 AT,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.