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 underdetermined 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.