Many inverse problems of practical interest are ill-posed in the sense that solutions do not depend continuously on data. To eeectively solve such problems, regularization methods are typically used. One problem associated with classical regularization methods is that the solution may be oversmoothed in the process. We present an alternative \local regularization" approach in which a decomposit...

In Tikhonov-Phillips regularization of general form the given ill-posed linear system is replaced by a Least Squares problem including a minimization of the solution vector x, relative to a seminorm ‖Lx‖2 with some regularization matrix L. Based on the finite difference matrix Lk, given by a discretization of the first or second derivative, we introduce the seminorm ‖LkD x̃ x‖2 where the diagona...

We consider a nonhomogeneous first-order evolution equation governed by maximal monotone operator $ A in Hilbert space the presence of Tikhonov regularization term. study existence and strong convergence weak solutions to such systems. With boundedness conditions on central path or solution trajectory, without assuming zero set be nonempty with suitable assumptions coefficient, we prove that sy...