Iterations of Some Algorithms for Nonlinear Fitting

By dragging the starting point with the locator, you can see how three nonlinear fitting algorithms proceed and how many steps they need. The three algorithms considered are the Levenberg–Marquardt, Newton, and gradient methods.

In our example, we fit a logistic model to a yeast culture data [1]. The data is as follows: 9.6, 18.3, 29.0, 47.2, 71.1, 119.1, 174.6, 257.3, 350.7, 441.0, 513.3, 559.7, 594.8, 629.4, 640.8, 651.1, 655.9, 659.6, 661.8.

These figures are the size of the yeast culture measured at 0, 1, 2, …, 18 (hours). The logistic model is . The background plot is a contour plot of the sum of the squared residuals with respect to and . The solution of the fitting problem is the minimum point of the sum of the squared residuals (shown in red).