36.5 Search Stopping Parameters

A root finding procedure should stop when one of the following conditions is true:

• A multidimensional root has been found to within the user-specified precision.
• A user-specified maximum number of iterations has been reached.
• An error has occurred.

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.

Function: int gsl_multiroot_test_delta (const gsl_vector * dx, const gsl_vector * x, double epsabs, double epsrel)

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_SUCCESS if the following condition is achieved,

|dx_i| < epsabs + epsrel |x_i|

for each component of x and returns GSL_CONTINUE otherwise.

Function: int gsl_multiroot_test_residual (const gsl_vector * f, double epsabs)

This function tests the residual value f against the absolute error bound epsabs. The test returns GSL_SUCCESS if the following condition is achieved,

\sum_i |f_i| < epsabs

and returns GSL_CONTINUE otherwise. 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.