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 Results for DC.creator="P." AND DC.creator="T." AND DC.creator="Boggs" in section 8.1.4 of volume C
Recommendations
Prince, E. and Boggs, P. T.  International Tables for Crystallography (2006). Vol. C, Section 8.1.4.5, p. 685 [ doi:10.1107/97809553602060000609 ]
... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 685 International Union of Crystallography 2006 | home | resources | advanced search ...

Stopping rules
Prince, E. and Boggs, P. T.  International Tables for Crystallography (2006). Vol. C, Section 8.1.4.4, pp. 684-685 [ doi:10.1107/97809553602060000609 ]
... satisfy a relative error test with respect to a tolerance T if Roughly speaking, if T is of the form then a and b agree to ... reasonably well with the predicted reduction. A typical value for T should be 10-4, although the value again depends ...

Quasi-Newton, or secant, methods
Prince, E. and Boggs, P. T.  International Tables for Crystallography (2006). Vol. C, Section 8.1.4.3, pp. 683-684 [ doi:10.1107/97809553602060000609 ]
... the gradient of S and is the Hessian matrix, the p p symmetric matrix of second partial derivatives, . Thus, d is ... d; (4) update Hc by Hc + g(xc)g(xc)T/dTg(xc) + qqT/[alpha]qTd (see Nash & Sofer, 1995), ...

Trust-region methods - the Levenberg-Marquardt algorithm
Prince, E. and Boggs, P. T.  International Tables for Crystallography (2006). Vol. C, Section 8.1.4.2, p. 683 [ doi:10.1107/97809553602060000609 ]
... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 683 International Union of Crystallography 2006 | home | resources | advanced search ...

The Gauss-Newton algorithm
Prince, E. and Boggs, P. T.  International Tables for Crystallography (2006). Vol. C, Section 8.1.4.1, p. 683 [ doi:10.1107/97809553602060000609 ]
... undefined if the rank of the Jacobian, , is less than p. J(x) usually has rank p near the solution, but it may be rank deficient far ... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 683 International Union of Crystallography 2006 | home | resources | advanced ...

Methods for nonlinear least squares
Prince, E. and Boggs, P. T.  International Tables for Crystallography (2006). Vol. C, Section 8.1.4, pp. 682-685 [ doi:10.1107/97809553602060000609 ]
... find the minimum of where x is a vector of p parameters, and M(x) represents a set of model functions ... undefined if the rank of the Jacobian, , is less than p. J(x) usually has rank p near the solution, but it may be rank deficient ...

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