Condition number of the W-weighted Drazin inverse

摘要

In this paper, we get the explicit condition number formulas for the W-weighted Drazin inverse of a rectangular matrix using the Schur decomposition and the spectral norm. We characterize the spectral norm and the Frobenius norm of the relative condition number of the W-weighted Drazin inverse, and the level-2 condition number of the W-weighted Drazin inverse. The sensitivity for the W-weighted Drazin inverse solution of linear systems is presented. We also present the structured perturbation of the W-weighted Drazin inverse.