An improved first order local regularization method for ill-posed Volterra equations

Future-Sequential Regularization Methods for Ill-Posed Volterra Equations ∗ Applications to the Inverse Heat Conduction Problem

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck’s ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed first-kind Volterra equation is seen to be the limit of a sequence of solutions of we...

Local Regularization Methods for the Stabilization of Ill-Posed Volterra Problems

Solution of Ill-Posed Volterra Equations via Variable-Smoothing Tikhonov Regularization

We consider a “local” Tikhonov regularization method for ill-posed Volterra problems. In addition to leading to efficient numerical schemes for inverse problems of this type, a feature of the method is that one may impose varying amounts of local smoothness on the solution, i.e., more regularization may be applied in some regions of the solution’s domain, and less in others. Here we present pro...

An Improved Version of Marti's Method for Solving Ill-Posed Linear Integral Equations

We propose an algorithm for solving linear integral equations of the first kind that can be viewed as a variant of Marti's method; as opposed to that method, our algorithm leads to optimal convergence rates (also with noisy data).

A regularization method for ill-posed bilevel optimization problems

We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value error estimates.