Geodesic
A numerical method of fitting a multiparameter nonlinear function to experimental data in the $L_1$ norm
Applications of Mathematics, Tome 33 (1988) no. 3, pp. 161-170
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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.
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.
DOI : 10.21136/AM.1988.104299
Classification : 65D10, 65K05
Keywords: nonlinear function; adjustment of parameters by $L_1$ norm; photon correlation spectroscopy; analysis of experimental data 
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Jakeš, Jaromír. A numerical method of fitting a multiparameter nonlinear function to experimental data in the $L_1$ norm. Applications of Mathematics, Tome 33 (1988) no. 3, pp. 161-170. doi: 10.21136/AM.1988.104299

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