ON THE LEAST-SQUARES DETERMINATION OF LATTICE DIMENSIONS - A MODIFIED SINGULAR VALUE DECOMPOSITION APPROACH TO ILL-CONDITIONED CASES

A modification is described of the singular value decomposition (SVD) method suitable for under-determined linear least squares (LLS). When a set of data to be fitted is incomplete and does not allow an independent determination of all model parameters, the modified method automatically merges a previously available approximate solution into the LLS results. The solution so produced is more appropriate to the particular problem than the usual SVD solution, while still being a LLS estimate of the whole set of parameters. The method is discussed with reference to the LLS determination of unit-cell dimensions during the step-by-step assignment of h, k, l indices of a diffraction pattern.