Optimal regularization of the inverse heat-conduction problem

The solution of the inverse heat conduction problem is obtained using dynamic programming and generalized cross-validation to estimate the optimal regularization parameter. Generalized cross-validation is appealing because it uses only the data to estimate the optimal value of the regularization parameter. The calculations for generalized cross-validation are performed as an extension of dynamic programming. A discussion of the problem and a brief outline of the computational steps are given. Several numerical examples are included to demonstrate the validity and limitations of the method.