110420 NONLIN: Nonlinear Least-Squares Curve Fitting Program Version: October 1979 Author: Fred Wood, Standard Oil Company, Chicago, IL Submitted by: David Zarnow, U.S. Naval Avionics Center, Indianapolis, IN Operating System: See note below Source Language: See note below Memory Required: 70K user partitioned Keywords: Statistics Abstract: This program allows the user to estimate the coefficients of a nonlinear equation such as Y = A/(x + B)2 and Y = AxB = C_equations that are nonlinear in the coefficients. An iterative technique is used; the estimates at each iteration are obtained by Marquardt's Maximum Neighborhood Method which combines the Gauss (Taylor Series) Method and the Method of Steepest Descent. Since numerous forms of equations can be used, the user must specify the form by providing a subroutine to compute the values of the equation's coefficients. In addition, the user must provide a control card, a format card for reading data, and estimates of the starting values of the coefficients. The output of the program is a printed report which includes a description of the problem, the starting values of the coefficients, the size of the incremental steps, a summary of each iteration, and a summary of the final fit (in terms similar to those in the Linear Least-Squares Curve Fitting Program, DECUS No. 11-419). The statistics calculated include the number of observations, the number of coefficients, the residual degrees of freedom, the maximum and minimum value of the dependent variable as well as its range, the standard error and t-value for each coefficient, the residual sum of squares, the residual mean square, and the residual root mean square. Provisions are made to run multiple programs as well as different equations using the same data. The program as dimensioned (70K) will handle up to 20 variables and 170 observations. Information is given in the program listings on which dimensions to change in order to reduce the overall dimensions or to increase either the number of variables and/or the number of observations which the program will handle. Notes: Operating systems the program runs on are IAS V2.0+ with support for PLAS Directives, RSX-11M V3.0+. Source language the program is written in is FORTRAN IV V2.04C or later with virtual array support. Media (Service Charge Code): User's Manual (EA), 600' Magnetic Tape (MA) Format: FILES-11

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