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Manuscript Title: A procedure for nonlinear least squares refinement in adverse practical conditions.
Authors: J. Lang, R. Muller
Program title: NONLINEAR LEAST SQUARES FIT
Catalogue identifier: ABGA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)79
Programming language: Fortran.
Computer: CDC 6400/6500.
Operating system: SCOPE 3.2, RUN-COMPILER.
RAM: 8K words
Word size: 60
Keywords: General purpose, Nonlinear least Squares Fit, Linearization of Normal equations, Iterative solution.
Classification: 4.9.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 20/11/72 See below

Nature of problem:
To determine optimum values of a set of parameters for the best agreement (in a least squares sense) between a given set of (experimental) values and corresponding calculated (theoretical) values where these values may be nonlinearly dependent on the parameters.

Solution method:
The minimum of the sum of the squared deviations of the experimental and theoretical values is found by iteration. The normal equations are linearized and transformed to the principal axis system. If in any iteration ill-conditioning yields a large correction of the parameters, the admissible variations are restricted to a hypercube with sides parallel to the principal axis.

Unusual features:
None

Running time:
2 seconds on the CDC 6400/6500 system for 6 parameters and 50 data points. The running time depends strongly, of course, on the number of parameters and measured points, the number of iterations needed and on how time consuming the evaluation of the function to be fitted is.

CORRECTION SUMMARY
Manuscript Title: A procedure for nonlinear least squares refinement in adverse practical conditions. (C.P.C. 2(1971)79).
Authors: J. Lang, R. Muller
Program title: 000A CORRECTION 20/11/72
Catalogue identifier: ABGA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)308
Classification: 4.9.