A stopping rule for the conjugate gradient regularization method for ill-posed problems

Abstract

We present a novel parameter choice strategy for the conjugate gradient regularization algorithm which does not assume a priori information about the magnitude of the measurement error. Our approach imitates the truncated singular value decomposition within the Krylov subspaces associated with the normal equations. Conjugate gradient is implemented using the Lanczos bidiagonalization process with reorthogonalization. We compare our method with one proposed by Hanke and Raus and illustrate its performance with numerical experiments, including an inverse problem of acoustic source detection.