Output least squares stability in elliptic systems

摘要

In this paper the stability of the solutions of parameter estimation problems in their output least squares formulation is analyzed. The concepts of output least squares stability (OLS stability) is defined and sufficient conditions for this property are proved for abstract elliptic equations. These results are applied to the estimation of the diffusion, convection, and friction coefficient in second-order elliptic equations inℝn,n=2, 3.Results on Tikhonov regularization in a nonlinear setting are also give