The efficient calculation of the normal matrix in least-squares refinement of macromolecular structures

The optimization procedure with the greatest power of convergence is the full-matrix method. This method has not been utilized to a great extent in macromolecular refinement because of the great cost of both calculating and inverting the 'normal' matrix. This paper describes an algorithm that can calculate this matrix in a relatively short amount of computer time. The procedure requires two Fourier transforms, which can be performed with the fast-Fourier transformation (FFT) algorithm, as well as a large number of simple function products.