Some questions about interpolation...

[Aupetit Mickael]

Hello,

my name is Michael Aupetit, I'm a PhD student in the field
 of Artificial Neural Networks. I'm very interested by interpolation
technics. 

I've heard about "natural Neighbours"; "NURBS" and some 
other technics, but I fear these technics are not able to deal with
high dimensional input spaces (as we found in ANNs) with reasonable
time consuming and complexity of operations (e.g. for example,how 
to calculate vector product used in Natural Neighbour Interpolation, 
while the dimension of vectors is higher than 3?).

So, I have three questions:

Hypothesis: 
I have the p-dimensional Delaunay triangulation of n data
points. And I know the Jacobian (gradient) and possibly the Hessian 
(curvature) in each data point.

1) Does it exist any interpolation method able to deal with high
dimension (at least more than 5) that is C1 or C2 where ever? 
Could you send me references?

2) What is the complexity of existing interpolation technics according 
to n (the number of data points that support the interpolation) and p 
(the dimension of the input space) or other parameters? 

3) Does it exist "standard" tests to establish that an interpolation 
method is "good" or "bad"? (e.g. for example, we could imagine an 
interpolation method able to pass through all data points with a 1st
order continuity where ever, but with a not desired behavior between
data points, as "holly" or "gap" between them even if they are 
theoretically in the same plan according to their respective Jacobian...) 
 


Thank you for your help

Sorry if I've already contacted you by another way.

Michael Aupetit
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