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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 hi. If the computation converged, let n denote the number of Newton iterations needed. Then the new step size hi+1 will be selected as follows:

hi+1 = ì
ï
í
ï
î
hi·hdec
if not converged
hi·hinc
if converged and n < nthr
hi
otherwise
(22)

where hdec < 1, hinc > 1 and nthr are constants which are experimentally determined.