Fast Numerically Stable Computations for Generalized Linear Least Squares Problems

The generalized linear least squares problem is treated here as a linear least squares problem with linear equality constraints. Advantage is taken of this formulation to produce a numerically stable algorithm based on plane rotations which is designed for fast computation, especially for large structured problems. The algorithm can be made to handle any rank deficiency in the matrices. A rounding error analysis and operation counts are given. The use of nonunitary transformations is considered.