Orders of convergence for superlinearly convergent chaotic iterations (Q1179545)

If on computers with multiprocessors individual processors are allowed to proceed without waiting for each other it is natural to consider so- called chaotic iterations for computations on such computers. The author proves a theorem giving conditions for superlinear convergence of chaotic iterations in an appropriate setting. The theorem also contains a statement on the \(R\)-order of the sequence generated. The author remarks that the new theorem can be regarded as giving a relationship between the speed of convergence of the total step or Gauss- Jacobi method for a given (in general nonlinear) mapping and chaotic iteration methods.