Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

Abstract

One of the most successful methods for solving the least-squares problem minx∥Ax−b∥2 with a highly ill-conditioned or rank deficient coefficient matrix A is the method of Tikhonov regularization. In this paper, we derive the normwise, mixed and componentwise condition numbers and componentwise perturbation bounds for the Tikhonov regularization. Our results are sharper than the known results. Some numerical examples are given to illustrate our results. Copyright © 2010 John Wiley & Sons, Ltd.