Nonlinear Least-Squares Fitting of First-Order Rate Coefficients Comparison between the Gauss-Seidel Method and Swain's Kore Program

摘要

Swain and coworkers at MIT recently composed a 92-statement Fortran computer program to evaluate first-order rate coefficients from kinetic data. The program is called KORE (kinetic analysis using overrelaxation); the use of the overrelaxation factor accelerates the convergence of the calculation which Swain feels would be of advantage for any question fit with a least-squares method. To show the utility of the overrelaxation factor, Swain purposely used poor data to show that the KORE program converged while a much longer program by DeTar (LSKIN 1) did not converge. The authors have a general least-squares program based on the Gauss-Seidel method that was written in 1960 at Los Alamos Scientific Laboratory, and has been widely used in other Laboratories based on the number of citations in the Science Citation Index. It was thought that it might prove useful to see how this program handled the purposedly poor data Swain used to show the merit of the overrelaxation method. It was found that the Gauss-Seidel program converged unlike DeTar's program, so it is uncertain what advantage the overrelaxation factor contributes for the general least-squares method. Nevertheless, Swain's short program is still extremely useful for fitting first-order kinetic data which microcomputers, and Hovanec has adapted Swain's program in BASIC for the HP85 and APPLE II Plus computers.