82) Deriving Distributed Recursion

▤ Summary

That note explained it as an issue of quality balancing, but the method does have some mathematical underpinnings which can provide further insight into how it works, particularly if you are the sort of person who likes to see the equations . (If the derivative term is still hard to solve, you can repeat the process recursively, doing an expansion to approximate its behaviour until you have something you can calculate (Although it would be trendier to apply machine learning, a neural net or some other AI technique, rather than actually working through the layers of maths.) We could stop here and use this design in an SLP model, using estimated qualities and quantities for all the blends to create our linear approximations - but the equation can be manipulated further to make something that will recurse better - with fewer assumed values and better scaling. This is a better equation for SLP for several reasons: - Quantities can make for large co-efficients, and so result in poorly scaled matrices - Distributions are often more stable in the solution than amounts. So, while SLP with Distributed Recursion, like most other non-linear optimization techniques relies on heuristics to move from one approximation to another in search of a solution to the full problem, its not all rules of thumb - there are some good mathematical underpinnings inside the box too.

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