Accuracy and stability of the null space method for solving the equality constrained least squares problem
The stability of null space methods for solving the linear least squares problem subject to equality constraints (the LSE problem) is proved via a detailed rounding error analysis. A normwise perturbation theory for the LSE problem is presented. A perturbation bound is derived but it is shown that the bound does not yield a condition number for the LSE problem, since it is not attainable. By modifying the analysis an almost sharp bound is derived that yields a quantity that is within a small constant factor of the condition number for the LSE problem. The quantity LSE\(_-\)err is determined which can be used as an approximate forward error bound for the null space method for solving the LSE problem and, in particular, for use with the driver routine ``xgglse.f'' in LAPACK.
scientific article; zbMATH DE number 1275241