  In this article we investigate the connection between regularization theory
for inverse problems and dynamic programming theory. This is done by developing
two new regularization methods, based on dynamic programming techniques. The
aim of these methods is to obtain stable approximations to the solution of
linear inverse ill-posed problems. We follow two different approaches and
derive a continuous and a discrete regularization method. Regularization
properties for both methods are proved as well as rates of convergence. A
numerical benchmark problem concerning integral operators with convolution
kernels is used to illustrate the theoretical results.
