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From: Jeronimo Pellegrini (pellegrini_at_[hidden])
Date: 2006-06-29 06:43:21

On Thu, Jun 29, 2006 at 08:20:34AM +0200, Gunter Winkler wrote:
> 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?

They are usually sparse, particularly in the problems I am working with.

> 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.

I will check it out, thank you!