Comparison of different versions of the conjugate gradient method of function estimation

The inverse problem of estimating the spatial and transient variations of the heat transfer coefficient at the surface of a plate, with no information regarding its functional form, is solved by applying the conjugate gradient method with adjoint problem. Three different versions of this method, corresponding to different procedures of computing the search direction, are applied to the solution of the present inverse problem. They include the Fletcher-Reeves, Polak-Ribiere, and Powell-Beale versions. Such versions arp compared for test cases involving different numbers of sensors, levels of measurement errors, and initial guesses used for the iterative procedure.