Efficiency and Accuracy in Quadratic Curve Fitting: A Comparative Analysis of Optimization Techniques

In this paper, we investigate an optimization methods might be applied for solving curve fitting by making use of a quadratic model. To discover the ideal parameters for the quadratic model, synthetic experimental data is generated, and then two unique optimization approaches, namely differential evolution and the Nelder-Mead algorithm, are applied to the problem in order to find the optimal values for those parameters. The mean squared error as well as the correlation coefficient are both metrics that are incorporated into the objective function. When the results of these algorithms are compared, trade-offs between the rate of convergence and the quality of the fit are revealed. This work sheds light on the necessity of selecting proper optimization algorithms for specific circumstances and provides insights into the balance that must be struck between accurate curve fitting and efficient use of computational resources in the process of curve fitting.