I am trying to implement Minimum Discarded Fill (MDF) Ordering algorithm for incomplete matrix factorization. The algorithm description is here on page 60 Preconditioning Techniques for a Newton–Krylov Algorithm for the Compressible Navier–Stokes Equations.

There is a thing that I don't understand. For initialization I should use Algorithm 7 (page 62)

Compute the discard value for all nodes vj in the graph of A0 using Algorithm 7

But this algorithm uses the value that is calculated later. We have only variables with k-index

Compute the discard value, discard(vk) = ||Fk||F using the following iterations

And there is the k+1-index variable


I can’t understand whether it is a recursion or something regarding iterative methods... if it will be easy for anyone to understand this MDF algorithm, please tell me how to implement this moment.


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