A root finding procedure should stop when one of the following conditions is true:
The handling of these conditions is under user control. The functions below allow the user to test the precision of the current result in several standard ways.
This function tests for the convergence of the sequence by comparing the last step dx with the absolute error epsabs and relative error epsrel to the current position x. The test returns
GSL_SUCCESSif the following condition is achieved,|dx_i| < epsabs + epsrel |x_i|
for each component of x and returns
This function tests the residual value f against the absolute error bound epsabs. The test returns
GSL_SUCCESSif the following condition is achieved,\sum_i |f_i| < epsabs
GSL_CONTINUEotherwise. This criterion is suitable for situations where the precise location of the root, x, is unimportant provided a value can be found where the residual is small enough.