Iteration processes may be classified according to their asymptotic behavior. In particular a process is said to be linearly or quadratically convergent to a stationary solution if, for the error f~ = x, -x of the ith approximation x~, using a convenient norm, the respective bounds fl L+, ][ < 71 JJ fL Jl (0<7< D, [I f,+l [[ <~ 72 I1 f, I[ 2 are valid in a certain neighborhood of x. This definition states nothing concerning the behavior in the large, which is, in practice at least, as important as the asymptotic behavior.
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F. L. Bauer (1958) studied this question.