On the Convergence of the Generalized Linear Least Squares Algorithm

This paper considers the issue of parameter estimation for biomedical applications using nonuniformly sampled data. The generalized linear least squares (GLLS) algorithm, first introduced by Feng and Ho (1993), is used in the medical imaging community for removal of bias when the data defining the model are correlated. GLLS provides an efficient iterative linear algorithm for the solution of the non linear parameter estimation problem. This paper presents a theoretical discussion of GLLS and introduces use of both Gauss Newton and an alternating Gauss Newton for solution of the parameter estimation problem in nonlinear form. Numerical examples are presented to contrast the algorithms and emphasize aspects of the theoretical discussion.AMS subject classification (2000) 65F10.R. A. Renaut: This work was partially supported by the Arizona Center for Alzheimer’s Disease Research, by NIH grant EB 2553301 and for the second author by NSF CMG-02223.Received December 2003. Revised November 2004. Communicated by Lars Eldén.