Evaluation of absorption coefficient based on proper solution space

This note is concerned with a new method for the evaluation of an unknown coefficient in a parabolic equation. The method starts with an initial guess for the unknown function and obtains corrections to the assumed value at every iteration. The updating step is the new feature of the present algorithm. The method treats the error field which has the appropriate (zero) Dirichlet boundary conditions. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown function. A number of numerical examples are used to show the applicability of the method.