MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user’s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon- Fletcher-Goldfarb-Shanno (BFGS) variable- metric method for unconstrained minimization in conjunction with a one dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

This program was written by Scott A. Hill of Langley Research Center. For further information, access the Technical Support Package (TSP) free on-line at under the Software category. LAR-17091-1

NASA Tech Briefs Magazine

This article first appeared in the December, 2005 issue of NASA Tech Briefs Magazine.

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