An accelerated alternating iterative algorithm for data completion problems connected with Helmholtz equation

This paper deals with an inverse problem governed by the Helmholtz equation. It consists in recovering lackingdata on a part of the boundary based on the Cauchy data on the other part. We propose an optimal choice of the relaxationparameter calculated dynamically at each iteration. This choice of relaxation parameter ensures convergence without priordetermination of the interval of the relaxation factor required in our previous work. The numerous numerical example showsthat the number of iterations is drastically reduced and thus, our new relaxed algorithm guarantees the convergence for allwavenumber k and gives an automatic acceleration without any intervention of the user.