A Gauss-Seidel least-squares refinement procedure with rigid-group and parameter restraint capabilities

A fast Gauss-Seidel least-squares procedure (FGLS) has been developed for crystallographic refinement of atom parameters in large asymmetric units. The procedure combines the minimum matrix requirements and the rapid convergence of the Gauss-Seidel algorithm with rigid-group constraint and subsidiary parameter elastic restraint capabilities. As the procedure is essentially block diagonal, considerable computational efficiency is achieved by determining contributions from one atom to all reflections at a time, instead of the usual practice of determining the contributions from all atoms to each reflection in turn. Application of the method to a 1104-atom protein at 2.5 Å resolution is described.