A new scheme for calculating weights and describing correlations in nonlinear least-squares fits

Journal Article · Fri Mar 01 04:00:00 EST 1996 · Computers in Physics

DOI:https://doi.org/10.1063/1.168569· OSTI ID:279722

Hessler, J P ^[1]; Current, D H ^[2]; Ogren, P J ^[3]

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1. Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
2. Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859 (United States)
3. Department of Chemistry, Earlham College, Richmond, Indiana 47374 (United States)

The equations for nonlinear least-squares analysis are reformulated in terms of dimensionless vectors and matrices. The diagonal elements of a dimensionless curvature matrix give the relative weights of the fit variables. Eigenvectors and eigenvalues of this matrix are used to describe the correlations between all of the parameters, and bivariant correlation coefficients may be calculated directly from its matrix elements. With the dimensionless formulation it is easy to compare confidence limits, correlations, and predictions based on the curvature matrix with results of Monte Carlo simulations. This provides a direct test of the parabolic approximation. Examples from a linear and biexponential model are presented to demonstrate these ideas. {copyright} {ital 1996 American Institute of Physics.}

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 279722
• Journal Information: Computers in Physics, Journal Name: Computers in Physics Journal Issue: 2 Vol. 10; ISSN 0894-1866; ISSN CPHYE2
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
CORRELATIONS
DATA ANALYSIS
EIGENVECTORS
LEAST SQUARE FIT
MATRICES
WEIGHTING FUNCTIONS