R_i'(θ) values, gradients, and Hessians

The partial and second partial derivatives of the relaxation equations of the set R'(θ) are different for each parameter of the vector θ. The vector representation of the gradient ∇R_i'(θ) and the matrix representation of the Hessian ∇²R_i'(θ) can be reconstructed from the individual elements presented in the next section.