This note is concerned with a new method for the solution of an elliptic
Inverse Heat Conduction Problem (IHCP). It considers an elliptic system where
no information is given at part of the boundary. The method is iterative in
nature. Starting with an initial guess for the missing boundary condition, the
algorithm obtains corrections to the assumed value at every iteration. The
updating part of the algorithm is the new feature of the present algorithm.
The algorithm shows good robustness to noise and can be used to obtain a good
estimate of the unknown boundary condition. A number of numerical examples are
used to show the applicability of the method.