Previous |  Up |  Next


Title: A numerical method of fitting a multiparameter nonlinear function to experimental data in the $L_1$ norm (English)
Author: Jakeš, Jaromír
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 33
Issue: 3
Year: 1988
Pages: 161-170
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: A numerical method of fitting a multiparameter function, non-linear in the parameters which are to be estimated, to the experimental data in the $L_1$ norm (i.e., by minimizing the sum of absolute values of errors of the experimental data) has been developed. This method starts with the least squares solution for the function and then minimizes the expression $\sum_i (x^2_i + a^2)^{1/2}$, where $x_i$ is the error of the $i$-th experimental datum, starting with an $a$ comparable with the root-mean-square error of the least squares solution and then decreasing it gradually to a negligibly small value, which yields the desired solution. The solution for each fixed $a$ is searched by using the Hessian matrix. If necessary, a suitable damping of corrections is initially used. Examples are given of an application of the method to the analysis of some data from the field of photon correlation spectroscopy. (English)
Keyword: nonlinear function
Keyword: adjustment of parameters by $L_1$ norm
Keyword: photon correlation spectroscopy
Keyword: analysis of experimental data
MSC: 65D10
MSC: 65K05
idZBL: Zbl 0654.65010
idMR: MR0944780
DOI: 10.21136/AM.1988.104299
Date available: 2008-05-20T18:34:27Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] K. Zimmermann M. Delaye P. Licinio: Analysis of multiexponential decay by a linear programming method: Application to light scattering spectroscopy.J. Chem. Phys. 82 (1985) 2228. 10.1063/1.448316
Reference: [2] G. B. Dantzig: Linear Programming and Extensions.Princeton University Press, Princeton, New Jersey 1963. Zbl 0108.33103, MR 0201189
Reference: [3] K. Zimmermann J. Jakeš: .Unpublished results.
Reference: [4] J. Jakeš P. Štěpánek: .To be published.
Reference: [5] A. J. Pope: Two approaches to nonlinear least squares adjustments.Can. Surveyor 28 (1974) 663. 10.1139/tcs-1974-0111
Reference: [6] M. J. Box: A comparison of several current optimization methods, and the use of transformations in constrained problems.Computer J. 9 (1966) 67. Zbl 0146.13304, MR 0192645, 10.1093/comjnl/9.1.67
Reference: [7] B. A. Murtagh R. W. H. Sargent: Computational experience with quadratically convergent minimisation methods.Computer J. 13 (1970) 185. MR 0266403, 10.1093/comjnl/13.2.185
Reference: [8] K. Levenberg: A method for the solution of certain non-linear problems in least squares.Quart. Appl. Mathematics 2 (1944) 164. Zbl 0063.03501, MR 0010666, 10.1090/qam/10666
Reference: [9] D. W. Marquardt: An algorithm for least-squares estimation of nonlinear parameters.J. Soc. Indust. Appl. Math. 11 (1963) 431. Zbl 0112.10505, MR 0153071, 10.1137/0111030
Reference: [10] P. Bloomfield W. L. Steiger: Least Absolute Deviations. Theory, Applications, and Algorithms.Birkhäuser, Boston-Basel-Stuttgart 1983. MR 0748483
Reference: [11] T. S. Arthanari Y. Dodge: Mathematical Programming in Statistics.Wiley, New York 1981. MR 0607328


Files Size Format View
AplMat_33-1988-3_1.pdf 1.603Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo