The module LSQ is for unconstrained linear least-squares fitting. It is based upon Applied Statistics algorithm AS 274 (see comments at the start of the module). A planar-rotation algorithm is used to update the QR- factorization. This makes it suitable for updating regressions as more data become available. The module contains a test for singularities which is simpler and quicker than calculating the singular-value decomposition. An important feature of the algorithm is that it does not square the condition number. The matrix X X is not formed. Hence it is suitable for ill- conditioned problems, such as fitting polynomials. By taking advantage of the MODULE facility, it has been possible to remove many of the arguments to routines. Apart from the new function VARPRD, and a back-substitution routine BKSUB2 which it calls, the routines behave as in AS 274.
