Test procedures and test problems for least squares algorithms

Numerous test problems have been introduced in the past twenty years for the purpose of studying and comparing least squares algorithms and computer programs. This paper discusses and classifies some of the useful test problems which have appeared in the literature. A recent large scale test procedure is briefly summarized. Several neat, mathematical examples are displayed. One of these, first introduced by Läuchli, is modified so that it can be solved by the method of inverting a matrix of correlation coefficients. Comparative results from running two types of problems on several different algorithms are given which illustrate some of the factors affecting computational accuracy: choice of algorithm, scaling of the data, tolerance parameters, and iterative refinement.