On the superlinear convergence of the successive approximations method
Successive approximation \(x_{k+1}= G(x_k)\) is considered and its high convergence order in terms of some spectral elements of \(G'(x^*)\) is examined. The author shows that the set of trajectories with high convergence orders is restricted to some affine subspaces, regardless of the nonlinearity of \(G\). The stability of the successive approximations under perturbations is also analyzed.
scientific article; zbMATH DE number 1812456