Appendix

We now prove the Theorem 1, which forms the basis for the dynamic algorithm. We begin by setting them equal. We can now directly match coefficients between (19) and (23), as they hold for any gradient values. As mentioned in Section 3.2, directly implementing the various recursive formulas of the dynamic In theory, the algorithm presented so far should be well suited for utilizing the massive parallel computation capabilities of a GPU. Similarly, each block depends exclusively on the blocks above it (up to the diagonal).