Tables for
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F, ch. 25.2, p. 719   | 1 | 2 |

Section Preconditioned conjugate-gradient minimization (1990)

D. E. Tronrudm* and L. F. Ten Eycky Preconditioned conjugate-gradient minimization (1990)

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This method of minimization (Axelsson & Barker, 1984[link]; Tronrud, 1992[link]) allows the direct inclusion of the diagonal elements of the second-derivative matrix and the indirect inclusion of its off-diagonal elements. An additional benefit is that it allows both positional parameters and B factors to be optimized in each cycle. Previously, one was required to hold one class of parameter fixed while the other was optimized. It is much more efficient and simpler for the user to optimize all parameters at once. This method, because it incorporates the diagonal elements directly, produces sets of B factors that agree with the diffraction data better than those from the simple conjugate-gradient method.


Axelsson, O. & Barker, V. (1984). Finite element solution of boundary value problems, ch. 1, pp. 1–63. Orlando: Academic Press.Google Scholar
Tronrud, D. E. (1992). Conjugate-direction minimization: an improved method for the refinement of macromolecules. Acta Cryst. A48, 912–916.Google Scholar

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