An acceleration device and standard-deviation estimates in least-squares refinements of crystal structures

Least-squares refinement of atomic positions and anisotropic vibrations is discussed. An approximation is described, for which most of the off-diagonal elements of the normal matrix need not be calculated, and an acceleration device is suggested. The effect of the matrix approximation upon standard-deviation estimates can be assessed, and similar considerations apply to standard deviations of combinations of parameters, calculated from the diagonal elements of the full variance matrix. Three tests of the acceleration device are described. 1. Definitions h