  The purpose of this study is to show some mathematical aspects of the adjoint
method that is a numerical method for the Cauchy problem, an inverse boundary
value problem. The adjoint method is an iterative method based on the
variational formulation, and the steepest descent method minimizes an objective
functional derived from our original problem. The conventional adjoint method
is time-consuming in numerical computations because of the Armijo criterion,
which is used to numerically determine the step size of the steepest descent
method. It is important to find explicit conditions for the convergence and the
optimal step size. Some theoretical results about the convergence for the
numerical method are obtained. Through numerical experiments, it is concluded
that our theories are effective.
