Perturbation Bounds Of The Moore-Penrose Inverse

The data of matrix A are input into the computer, which induces flopping errors. Thus, the accuracy computed solutions of A, for example, eigenvalue, singular value and least squares solution and so on, are actually ones of B = A+E to which A is perturbed. We measure distance between the true value and the computed value by norm of E = B - A. In this field, many workers have studied and obtained a lot of classical results.In this paper, we study the perturbation bounds of the Moore-Penrose inverse and weighted Moore-Penrose inverse, and get new perturbation bounds for the Moore-Penrose inverse and weighted Moore-Penrose inverse. In Chapter 3, we get the op-timal additive perturbation bounds of the Moore-Penrose inverse under the Frobenius norm. Chapter 4 investigate the additive perturbation bounds of the Moore-Penrose inverse under any unitarily invariant norm, which improve the bound Wedin have ob-tained. And in Chapter 5, we get new additive perturbation bounds of the weighted Moore-Penrose inverse, which improve the old results. In addition, the multiplicative perturbation bounds of the Moore-Penrose are given first.