A constrained approximation problem arising in parameter identification

Abstract : We pose and solve an extremal problem in the Hardy class H-2 of the disc, involving the best approximation of a function on a subarc of the circle by a H-2 function, subject to a constraint on its imaginary part on the complementary arc. A constructive algorithm is presented for the computation of such a best approximant, and the method is illustrated by a numerical example. The whole problem is motivated by boundary parameter identification problems arising in non-destructive control