The value, gradient, and Hessian dependency chain

The dependency chain which was outlined in the model-free chapter - that the chi-squared function is dependent on the transformed relaxation equations which are dependent on the relaxation equations which themselves are dependent on the spectral density functions - combine with the values, gradients, and Hessians to create a complex web of dependencies. The relationship between all the values, gradients, and Hessians are outlined in Figure 15.3.

Figure 15.3: Dependencies between the χ², transformed relaxation, relaxation, and spectral density equations, gradients, and Hessians.