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A versatile implementation of the Gauss-Newton minimization algorithm using MATLAB for Macintosh microcomputers
1Institute of Pharmacological Sciences, University of Milan, Italy.
Computer Methods and Programs in Biomedicine
|June 1, 1990
Summary
This study presents a versatile nonlinear least-squares fitting routine for MacMATLAB. The software numerically estimates derivatives and integrates differential equations, enabling flexible data analysis for various scientific functions.
Area of Science:
- Numerical Analysis
- Scientific Computing
- Software Development
Background:
- Nonlinear least-squares minimization is crucial for fitting complex models to data.
- Existing methods often require analytical derivatives, limiting applicability.
- MacMATLAB provides an interactive environment for scientific calculations.
Purpose of the Study:
- To develop and present a weighted nonlinear least-squares minimization routine for MacMATLAB.
- To create a flexible tool capable of fitting a wide range of nonlinear functions.
- To simplify the process by avoiding the need for analytical function differentiation.
Main Methods:
- Implementation of a weighted nonlinear least-squares minimization routine.
- Utilization of a subroutine for numerical derivative estimation.
- Inclusion of subroutines for numerical integration of ordinary differential equations.
- Development for the MacMATLAB environment.
Main Results:
- The routine successfully fits diverse nonlinear functions and differential equations.
- Numerical derivative estimation eliminates the need for analytical differentiation.
- Flexible error structure specification allows for weighted fitting.
- Graphical capabilities enable visual tracking of fitting progress.
Conclusions:
- The developed routine offers a powerful and flexible approach to nonlinear data fitting.
- It simplifies complex analyses by handling numerical differentiation and integration.
- The MacMATLAB implementation makes advanced fitting accessible to a wider user base.