Abstract
A modified version of the classical discrepancy principle
is formulated for use with generalized local regularization operators
of the form
for the approximate solution of linear inverse problems
in Banach space with deterministically modeled noise. The choice of the
local regularization parameter according to the
parameter selection strategy is shown to result in a class of convergent
regularization methods and a general rate of convergence is
provided. As an example, the theory is applied to establish convergence
and convergence rates for approximations obtained using a zeroth-order
local regularization scheme with the modified principle for solving
Volterra convolution equations in
,
. A numerical example is provided to illustrate the practical use and
effectiveness of the method.