Condition number for the w-weighted drazin inverse and its applications in the solution of rectangular linear system

Minimum property of condition numbers for the Drazin inverse and singular linear equations

“…In this note, we characterize the condition number of Drazin inverse and the Drazin inverse solution of singular linear systems. It is of interest to extend our results to the W-weighted Drazin inverse of a rectangular matrix [22][23][24][25][26][27][28][29] and the bounded linear operator [30][31][32].…”

Estimation of a condition number related to A(2)T,S

“…The following result is a generalization of results from [5] and [10]. Let (E n ) n be a sequence of perturbations of A fulfilling the condition (4), and let (f n ) n be a sequence of perturbations of b. If C(E n , f n ) is the corresponding absolute condition number and A…”

“…In [13], Y. Wei and H. Diao considered the condition number for the Drazin inverse and the Drazin inverse solution of singular linear system. X. Cui and H. Diao generalized the results of [13] and get the results of the condition number for the W -weighted Drazin inverse and the W -weighted Drazin inverse solution of a linear system in paper [4]. In [10], we extend the result obtained in [4] to linear bounded operators between Hilbert spaces.…”

“…X. Cui and H. Diao generalized the results of [13] and get the results of the condition number for the W -weighted Drazin inverse and the W -weighted Drazin inverse solution of a linear system in paper [4]. In [10], we extend the result obtained in [4] to linear bounded operators between Hilbert spaces. In [11], the authors established the condition number of the W -weighted Drazin inverse of a rectangular matrix by the Schur decomposition and the spectral norm.…”

“…Because all generalized inverses belong to outer inverse A (2) T,S with the prescribed range T and null space S, we are more interested in the condition numbers connected with the outer inverse A (2) T,S . In [5], H. Diao, M. Qin and Y. Wei investigated the condition number of the outer inverse A (2) T,S and the outer inverse A (2) T,S solution of a constrained linear system which extends the results in [13,4]. They gave the explicit formula of the condition number for the outer inverse A (2) T,S solution of a constrained linear system.…”