This monograph is a valuable contribution to the highly topical and extremly productive field
of regularisation methods for inverse and ill-posed problems. The author is an internationally …

Fixed point iterations play a central role in the design and the analysis of a large number of
optimization algorithms. We study a new iterative scheme in which the update is obtained by …

Driven by the needs from applications both in industry and other sciences, the field of
inverse problems has undergone a tremendous growth within the last two decades, where …

The quasi-reversibility method of solving the Cauchy problem for the Laplace equation in a
bounded domain Ω is considered. With the help of the Carleman estimation technique …

This paper proposes a solution method for identification problems in the context of contact
mechanics when overabundant data are available on a part Γ m of the domain boundary …

Two methods of level set type are proposed for solving the Cauchy problem for an elliptic
equation. Convergence and stability results for both methods are proven, characterizing the …

The paper is devoted to the derivation of a numerical method for expanding available
mechanical fields (stress vector and displacements) on a part of the boundary of a solid into …

Various strategies are available to construct iteratively a common fixed point of
nonexpansive operators by activating only a block of operators at each iteration. In the more …

Image inpainting or disocclusion, which refers to the process of restoring a damaged image
with missing information, has many applications in different fields. Different techniques can …

A classical ill-posed elliptic Cauchy problem is discussed. We consider the reconstruction of
the Dirichlet trace of the solution at the part of a boundary where no data are available. By …