On the convergence of the generalized linear least squares algorithm

C. Negoita, Rosemary Renaut

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)137-158
Number of pages22
JournalBIT Numerical Mathematics
Volume45
Issue number1
DOIs
StatePublished - Mar 2005

Fingerprint

Generalized Least Squares
Linear Algorithm
Linear Least Squares
Least Square Algorithm
Parameter estimation
Parameter Estimation
Gauss-Newton
Nonlinear Estimation
Biomedical Applications
Medical Imaging
Medical imaging
Iterative Algorithm
Numerical Examples
Model

Keywords

  • Generalized linear least squares
  • Iterative methods
  • Parameter estimation

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Computational Mathematics

Cite this

On the convergence of the generalized linear least squares algorithm. / Negoita, C.; Renaut, Rosemary.

In: BIT Numerical Mathematics, Vol. 45, No. 1, 03.2005, p. 137-158.

Research output: Contribution to journalArticle

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