Perturbations For The Generalized Inverse A_T,s² And Its Applications

In this paper, we investigate the perturbation bounds for the generalized inverseA_T,S² and its applications. By using the singular value decomposition and the CS decom-position, we obtain the perturbation bounds and the relative perturbation bounds forthe generalized inverse A_T,S²under the range and the null of A_T,S²perturbing. We alsogive the more precisely perturbation bounds under a certain condition. We discuss theapplications in the field of the relative errors of the solution of the nonlinear system.We investigate the perturbation bounds for the Moore-Penrose inverse of operator byusing the block of the operator. We present the perturbation bounds for the operator A under certain condition, and obtain the more precisely perturbation bounds under somemore stronger conditions. We investigate the applications in the area of the relativeerrors of the minimum norm least squares solution of the equation.