A minimal error conjugate gradient method for ill-posed problems

For the ill-posed operator equationTx=y in Hilbert space, we introduce a modification of the usual conjugate gradient method which minimizes the error, not the residual, at each step. Moreover, the error is minimized over the same finite-dimensional subspace that is associated with the usual method.This work was completed while the author was on leave at the University of Tennessee, Knoxville, Tennessee. Travel support from the Taft Committee and from the University of Tennessee is gratefully acknowledged.