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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 convergence of the minimization method using the following criteria:
GSL_SUCCESS
.
A general guideline for selecting the step tolerance is to choose xtol = 10^{-d} where d is the number of accurate decimal digits desired in the solution x. See Dennis and Schnabel for more information.
max
arguments help ensure the test doesn’t break down in
regions where x_i or \Phi(x) are close to 0.
If this test succeeds, info is set to 2 and the function
returns GSL_SUCCESS
.
A general guideline for choosing the gradient tolerance is to set
gtol = GSL_DBL_EPSILON^(1/3)
. See Dennis and Schnabel for
more information.
If none of the tests succeed, info is set to 0 and the
function returns GSL_CONTINUE
, indicating further iterations
are required.
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,
for each component of x and returns GSL_CONTINUE
otherwise.
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,
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.
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.
Next: High Level Driver, Previous: Iteration of the Minimization Algorithm, Up: Nonlinear Least-Squares Fitting [Index]