On 03-27-2011, at 4:51 PM, Aaron S. Meurer wrote:

> Well, I was under the impression that some numerical sparse data structures 
> used some kind of compression scheme that cannot be extended to symbolic 
> matrices.  This is just from what I have heard, though.
> 

I know quite a bit about numerical methods for sparse linear algebra. The 
different storage methods (data structures) are just different ways of storing 
and therefore accessing the non-zero entries in the sparse matrix.

> The algorithms have to do with numerical stability.  An algorithm that is 
> best for numerical stability with floating point numbers might not be the 
> best algorithm to prevent expression explosion with symbolic matrices.  The 
> algorithms are important, because they will have to be implemented along with 
> the sparse matrices (or else the implementation will be useless), and also 
> the algorithm chosen might depend on the data structure chosen (this is all 
> very abstract, but it's just some things to keep in mind).
> 

Very true. Methods that eliminate entries in a numerical situation might cause 
the symbolic case to just add new non-zero entries and add terms to existing 
entries (I've seen this happen). So, care has to be taken in algorithms for 
sparse symbolic matrices.

That said, a good sparse matrix implementation is needed for good handling of 
larger symbolic matrices.

Cheers,

Tim.

---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
http://about.me/tjlahey


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