A constrained approximation problem arising in parameter identification

Birgit Jacob (1, 2) , Juliette Leblond (3) , Jean-Paul Marmorat (4) , Jonathan R. Partington (2)

1 University of Paderborn
2 School of Mathematics [Leeds]
3 MIAOU - Mathematics and Computing in Automatic Control and Optimization for the User
4 CMA - Centre de Mathématiques Appliquées

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

Mots clés: Constrained approximation; Extremal problem; Parameter identification; Inverse problem; Laplace's equation

Domaines: Mathématiques [math]; Mathématiques appliquées

Birgit Jacob, Juliette Leblond, Jean-Paul Marmorat, Jonathan R. Partington. A constrained approximation problem arising in parameter identification. Linear Algebra and its Applications, 2002, 351-352, pp.487-500. ⟨10.1016/S0024-3795(01)00445-1⟩. ⟨hal-00504824⟩