Conjugate Gradient Type Methods for Ill-Posed Problems Hanke Martin

The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Most of the results are as yet unpublished, or obscured in the Russian literature. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many moreThis Research Note presents a unifying analysis of an entire family of conjugate gradient type methods.

Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived