Levenberg-Marquardt routine

There are no changes required in the Newton-Gauss-Levenberg/Marquardt routine nglm3. 111, but we do need to implement equations (4.85) to (4.87) into the function Rcalc EqF ix. 111, computing the residuals. 

Instead of using standard non-linear fitting routines (such as the steepest descendent or the Levenberg-Marquardt routine [31 ]), in the speeial ease of the Laplacian curve it appears more convenient to adopt substantially the same approach as earlier used by Maze and Burnet [21, 32], which can be defined as an iterative linear method. 

We perform nonlinear fitting using the Levenberg-Marquardt method implemented in the MRQMIN routine [75], From the experimental end, eight families of data are involved, namely, x (T) and x jT) at four frequencies, taken from Ref. 64. From the theory end, we employ formulas (4.121)-(4.124) with the numerical dispersion factors. The results of fitting are presented in Figures 4.6 and 4.7 and Table I. 

Excel s multi-parameter non-linear least-squares routine. Solver, an implementation of the Levenberg-Marquardt algorithm, is a generally useful tool. In section 10.8a we describe an addition that can make it even more useful, and in section 10.8b we briefly indicate how you can call Solver from your macro. 

Many approaches have been devised to solve equation (14) or (15). In this study, the Levenberg-Marquardt (LM) method was used. This is because the LM method works well in practice and has become the standard of nonlinear least squares routines [31]. 

Figure 3 shows the dissolution kinetics and Table 4 summarises the dissolution parameters derived from the rapid and slow dissolution phases by fitting equation 2 to the experimental data using a non linear least squares fitting routine based on the Levenberg Marquardt method. Table 5 summarises the radiochemistry results with imcertainties. 

To calculate the values of AH and that best describe the folding curve, initial values of AH, ACp, Of and On are estimated, and Equation [6] is fitted to the experimentally observed values of the change in ellipticity as a function of temperature, by a nonlinear least-squares curve-fitting routine such as the Levenberg-Marquardt algorithm. Similar equations can be used to estimate the thermodynamics of folding of proteins and peptides that undergo folded multimer to unfolded monomer transitions. 

---