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

• Published in: Applied mathematics and computation Vol. 217; no. 7; pp. 3199 - 3206
• Main Authors: Liu, Gang, Lu, Shengqi, Chen, Juping, Xu, Wei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 2010; Elsevier
• Subjects: Algebra; Algebraic geometry; Calculus of variations and optimal control; Condition number; Exact sciences and technology; Generalized inverse [formula omitted]; Index; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Perturbation; Schur decomposition; Sciences and techniques of general use; Condition number; Schur decomposition; Index; Perturbation; Generalized inverse A T , S; Numerical linear algebra; Generalized inverse A; Decomposition method; Iterative method; Direct method; Numerical analysis; Linear system; Matrix inversion; Applied mathematics
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.08.052

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.