Non-linear least-squares fit method

The rapid development of computer technology has yielded powerful tools that make it possible for modem EIS analysis software not only to optimize an equivalent circuit, but also to produce much more reliable system parameters. For most EIS data analysis software, a non-linear least squares fitting method, developed by Marquardt and Levenberg, is commonly used. The NLLS Levenberg-Marquardt algorithm has become the basic engine of several data analysis programs. 

Following the determination of the hydrolytic rate constants of an epimeric pair of tricyclic nitriles (78) by a non-linear, least-squares fitting method, a novel eigenvalue-eigenvector analysis of the sensitivity coefficients permitted maximization of the kinetic dataJ ... 

A Fortran code based on a gradient searching non-linear least square fitting method (55) was deveioped and used to fit SANS intensities in an absolute scale. Quality of the fits is uniformly excellent for Plutonic micellar systems in their entire range of the diswdered micellar phases. As an illustration, foe calculated particle structure factor P(k), the inter-particle structure factor S(k) and foe absolute intensity distribution I(k) from a typical fit is shown in Figure 3 together with foe measured one. 

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