Abstract: A system and method for producing a mathematical model of a dynamic system using a large number of parameters to produce a mathematical model most efficiently. The system uses large numbers of parameters while reducing the need of additional real data from tests and decreasing computational time to reach satisfactory models of the dynamic systems. The system efficiently and precisely computes all matrices that define the dynamic system. In addition, sparse non-linear programming is used to solve, quickly and efficiently, the matrices used by the present invention. Therefore, the method produces a quadratically converging algorithm for solving parameter estimation problems.