Multidimensional and Multi-Parameter Fortran-Based Curve Fitting Tools

The Levenberg-Marquardt algorithm has become a popular method in nonlinear curve fitting works. In this paper, following the steps of Levenberg-Marquardt algorithm, we extend the framework of the algorithm to two and three dimensional real and complex functions. This work briefly describes the mathematics behind the algorithm, and also elaborates how to implement it using FORTRAN 95 programming language. The advantage of this algorithm, when it is extended to surfaces and complex functions, is that it makes researchers to have a better trust during fitting. It also improves the generalization and predictive performance of 2D and 3D real and complex functions.