Re: Simplify formula for iterative programming

* stefaan.lhermitte@xxxxxxxxxxxxxxxxxx:
>
> I am looking for the simplification of a formula to improve the
> calculation speed of my program. Therefore I want to simplify the
> following formula:
>
> H =3D Si (Sj ( sqrt [ (Ai - Aj)=B2 + (Bi - Bj)=B2 ] ) )

I'm just guessing here, but possibly the above means

H = Si[ Sj[ sqrt( (Ai-Aj)^2 + (Bi-Bj)^2 ) ] ] for i, j in 1...n

> n is not fixed, but it changes with every run for my program. Therefore
> for I am looking for a simplication of H in order to calculate it when
> my A and B get extendend by 1 element (n =3D n + 1).

let n' = n + 1

H' = H + Si[ sqrt( (Ai-An')^2 + (Bi-Bn')^2 ) ]

where H'-H is the sum of distances in the plane from the point
(a,b) = (An',Bn').

The question is then how this sum of distances varies as (a,b) is
varied: can the formula be reduced to involve just a few numbers?

I imagine n points spread out on a line, and the point (a, b) moving
on a parallell line. I hypothesize that the sum of distances then has
n minima. Which, if true, means that the formula requires on the order
of n numbers, except if special relationships between the points'
coordinates (e.g., constant spacing between the points) allows some
simplification -- which I gather is not the case here.

So, most probably, sorry: I don't think you can reduce that to a constant
time computation.

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