Defined in a way similar to sequence convergence. Cauchy Convergence Criterion: On the Convergence Definition of Function f(x) at Point x0. For any real number b>0, c > exists; 0, for any x 1, x2 satisfies 0.
Convergence and divergence of iterative algorithm
1, global convergence
For any X0∈[a, b], the sequence of points generated by the iterative formula Xk+ 1=φ(Xk) converges, that is, when k→∞, the limit of Xk tends to X*, then Xk+ 1=φ(Xk) is called in [a, b].
2. Local convergence
If X* exists in a neighborhood, r = {x || x-x *|| < δ}}, for any X0∈R, the convergence listed in Xk+ 1=φ(Xk) is called Xk+ 1=φ(Xk) converges to x *.