Hello !
I’m working on a paper and would like to improve the methods section by explaining a little more the update process during solving the FDK.

I know that the computation solve F(alpha)=0 using a Newton Raphson Method with a golden section line search. However, what I don’t know exactly is the detailed process to update variables in such a way to get F(alpha)=0. How is the alpha variable chosen ? On which hypotheses are the update based ?

I hope my question is clear enough… Thank you for your explanations !
Lauranne

The FDK solver works on a multi-variable domain, so in principle there is not a single alpha, but one variable for each FDK degree of freedom.
The standard multivariable Newton Raphson method uses the Jacobean matrix of the equation system at a given guess on the solution. This provides a linearization of the problem, which can be solved as a linear set of equations to provide a new, hopefully better, guess on the solution.
To increase the robustness of this standard Newton method, one can apply different ways of NOT using the linear equation solution directly, but instead searching in the direction of the linear solution; thereby the problem I reduced from a multivariable problem to a single variable, i.e., line search where alpha is a variable measuring how much of the full Newton step is taken. The FDK solver in AnyBody 6.0 uses a Golden Section search method and it estimates the derivatives (i.e. the Jacobian matrix) by a perturbation method.