### 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 language | English (US) |
---|---|

Pages (from-to) | 137-158 |

Number of pages | 22 |

Journal | BIT Numerical Mathematics |

Volume | 45 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2005 |

### Fingerprint

### 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

*BIT Numerical Mathematics*,

*45*(1), 137-158. https://doi.org/10.1007/s10543-005-2638-8

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

Research output: Contribution to journal › Article

*BIT Numerical Mathematics*, vol. 45, no. 1, pp. 137-158. https://doi.org/10.1007/s10543-005-2638-8

}

TY - JOUR

T1 - On the convergence of the generalized linear least squares algorithm

AU - Negoita, C.

AU - Renaut, Rosemary

PY - 2005/3

Y1 - 2005/3

N2 - 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.

AB - 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.

KW - Generalized linear least squares

KW - Iterative methods

KW - Parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=33644604835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644604835&partnerID=8YFLogxK

U2 - 10.1007/s10543-005-2638-8

DO - 10.1007/s10543-005-2638-8

M3 - Article

AN - SCOPUS:33644604835

VL - 45

SP - 137

EP - 158

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 1

ER -