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From: Gunter Winkler (guwi17_at_[hidden])
Date: 2006-06-29 02:20:34

On Wednesday 28 June 2006 16:50, Jeronimo Pellegrini wrote:
> > PS: Do you really want to use a 3d data structure? Or do you just need a
> > collection of 2d data?
> It's a representation of a function with three arguments (the transition
> probability function in a Markov Decision Process:
> int x int x int -> double).

Are these matrices/tensors actually dense or have a specific structure?

If such mappings occur in numerical applications one usually does not store
matrix/tensor but directly provides an "apply_to_vector" function that uses
some compressed form of the matrix. There are many interesting results about
"sparse grids" or "hierarchical matrices" ( that provide fast
multiplication (read: nearly O(N)) even with quite dense matrices.