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

- A minimum 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 current estimate of the best-fit parameters in several standard ways.

- Function:
*int***gsl_multifit_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_multifit_test_gradient***(const gsl_vector **`g`, double`epsabs`) This function tests the residual gradient

`g`against the absolute error bound`epsabs`. Mathematically, the gradient should be exactly zero at the minimum. The test returns`GSL_SUCCESS`

if the following condition is achieved,\sum_i |g_i| < epsabs

and returns

`GSL_CONTINUE`

otherwise. This criterion is suitable for situations where the precise location of the minimum,*x*, is unimportant provided a value can be found where the gradient is small enough.

- Function:
*int***gsl_multifit_gradient***(const gsl_matrix **`J`, const gsl_vector *`f`, gsl_vector *`g`) This function computes the gradient

`g`of*\Phi(x) = (1/2) ||F(x)||^2*from the Jacobian matrix*J*and the function values`f`, using the formula*g = J^T f*.