A local stability analysis of nonlinear inverse problems

摘要

The stability behaviour of a nonlinear inverse problem F(x) = y at a solution point x0 is discussed in a Hibert space setting. We give a definition of local ill-posedness of the problem. Moreover, we formulate conditions such that the local degree of ill-posednes sin x0 can be expressed by properties of the Frechet derivative F'(x0) at this point. In order to illustrate these theoretic ideas, the presented theory is applied to a specific class of nonlinear equations occurring for some parameter identification problems in differential equations.