Ritz-Regularization versus Least-Square-Regularization. Solution Methods for Integral Equations of the First Kind

Three principles of regularization methods are discussed (Tikhonov-, Ritz- and Galerkin-method), and it is shown that in the case of positive definite or of selfadjoint operators the Ritz- and the Galerkin-principles (the latter with non-real parameter) have better properties than the Tikhonov-principle.