Parameterization of regularization methods

It has been established in Chapter 2 that the condition (2.1.7) for positive perturbation parameters δ and h and regularization parameter α are su.cient for the operator regularization methods to be convergent to solutions of monotone and accretive operator equations. However, such a wide choice of parameters does not possess the regularizing properties in the sense of De.nition 5 (see Preface). Our aim in this chapter is to indicate the ways to .nd the functions α = α(δ, h), which solve this problem when δ → 0 and h → 0.