I have a problem with a static (time invariant, but spatially varying) field expressed only as a set of discrete set of values at some points of an arbitrarily shaped domain in 2 or 3 dimensions. For example, if I have a one-dimensional domain from 0 to 1, the field $u$ has values $u = -5,0,1$ corresponding to $x=0,0.5,1$, respectively, except in my case I have hundreds of nodes with value of field at each node given.
Is there any way I can transform these values using very few parameters such I can reconstruct this field? Can you please provide references too?
I am looking for a numerically feasible algorithm. Approximation is ok. I would prefer to read some theory behind the methods, then I can decide which to choose.