ABSTRACT
A variety of inverse problems in the natural sciences, including identification of coefficients, reconstruction of initial data, estimation of source functions, and discovery of boundary conditions, demand the solution of ill-posed operator equations or the evaluation of unbounded operators. Instability is a common feature of these inverse problems and special means, known as regularization or stabilization procedures, are required for their numerical solution. We survey some of the basic theories of Tikhonov’s regularization method and related stabilization techniques in a general Hilbert space context.
