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Stepsize control

Stepsize control is an important issue in these algorithms. Too small stepsizes lead to unnecessary work being done, while too big stepsizes can lead to losing details of the curve. An easily implementable and proven to be reliable method is convergence-dependent control.

Consider the computation of a next point using step size . If the computation converged, let denote the number of Newton iterations needed. Then the new step size will be selected as follows:

| (22)

where , and are constants which are experimentally determined.