<p>given a matrix of distances between points is there an algorithm for determining a set of n-dimensional points that has these distances? (or at least minimises the error) </p>

<p>sort of like a n-dimensional version of the turnpike problem.</p>

<p>The best I can come up with is using multidimensional scaling.</p>

I can't edit the original, because I don't have enough rep, but I've tried to restate the problem here.
The OP has an input NxN matrix of distances. He wants to create an output array, size N, of N-dimensional coordinates representing points, where the distance between each point is stored in the input matrix.
Note that this is not solvable in the general case:
Suppose I have a matrix like this
```
A  B  C  
A  x  1  2  
B     x  0  
C        x
```
A is 1 unit of distance (say 1 metre) away from B, and A is one metre away from C. But B and C are in the same spot.
In this particular case the minimal sum of errors is 1 metre, and there are an infinite variety of solutions which achieve that result