International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 96

Having defined the now universally adopted R factors (Booth, 1945b) as criteria of agreement between observed and calculated amplitudes or intensities, Booth proposed that R should be minimized with respect to the set of atomic coordinates by descending along the gradient of R in parameter space (Booth, 1947c,d). This `steepest descents' procedure was compared with Patterson methods by Cochran (1948d).
When calculating the necessary derivatives, Booth (1948a, 1949) used the formulae given above in connection with least squares. This method was implemented by Qurashi (1949) and by Vand (1948, 1951) with parameterrescaling modifications which made it very close to the leastsquares method (Cruickshank, 1950; Qurashi & Vand, 1953; Qurashi, 1953).
References
Booth, A. D. (1945b). An expression for following the process of refinement in Xray structure analysis using Fourier series. Philos. Mag. 36, 609–615.Booth, A. D. (1947c). A new refinement technique for Xray structure analysis. J. Chem. Phys. 15, 415–416.
Booth, A. D. (1947d). Application of the method of steepest descents to Xray structure analysis. Nature (London), 160, 196.
Booth, A. D. (1948a). A new Fourier refinement technique. Nature (London), 161, 765–766.
Booth, A. D. (1949). The refinement of atomic parameters by the technique known in Xray crystallography as `the method of steepest descents'. Proc. R. Soc. London Ser. A, 197, 336–355.
Cochran, W. (1948d). Xray analysis and the method of steepest descents. Acta Cryst. 1, 273.
Cruickshank, D. W. J. (1950). The convergence of the leastsquares and Fourier refinement methods. Acta Cryst. 3, 10–13.
Qurashi, M. M. (1949). Optimal conditions for convergence of steepest descents as applied to structure determination. Acta Cryst. 2, 404–409.
Qurashi, M. M. (1953). An analysis of the efficiency of convergence of different methods of structure determination. I. The methods of least squares and steepest descents: centrosymmetric case. Acta Cryst. 6, 577–588.
Qurashi, M. M. & Vand, V. (1953). Weighting of the leastsquares and steepestdescents methods in the initial stages of the crystalstructure determination. Acta Cryst. 6, 341–349.
Vand, V. (1948). Method of steepest descents: improved formula for Xray analysis. Nature (London), 161, 600–601.
Vand, V. (1951). A simplified method of steepest descents. Acta Cryst. 4, 285–286.