A minimization 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 current estimate of the best-fit parameters 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 gradient g against the absolute error bound epsabs. Mathematically, the gradient should be exactly zero at the minimum. The test returns
GSL_SUCCESSif the following condition is achieved,\sum_i |g_i| < epsabs
GSL_CONTINUEotherwise. 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.
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.