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Re: [glas] vector space, banach space and hilbert space concepts

From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 2005-03-30 01:17:16

Matthias Troyer wrote:

> Hi Karl,
> On Mar 29, 2005, at 7:32 AM, Karl Meerbergen wrote:
>> I'd rather develop a concept that deals with the creation of objects
>> using dimensional or size information, e.g. DimensionConstructible,
>> which is orthogonal to the VectorSpace, Group, etc concepts. The
>> latter merely describe mathematical properties, while the former
>> describes the construction of a new vector or matrix from its
>> dimensional data. This could be the matrix size, a fixed sparse
>> structure, data about how to distribute the data over a network, etc.
> I take it that DimensionConstructible does not just construct the
> object from a dimension parameter (vector length) but is more
> generally a factory for objects, e.g. distributed vectors or higher
> dimensional arrays.

Yes. That is what I meant.

>> For example, an iterative method that does not require the creation
>> of new vectors (or matrices), may require the objects to be models of
>> HilbertSpace. A method as BiCGStab needs auxiliary vectors, for which
>> the creation of new vectors (or matrices) is needed. Such vectors
>> should be models of DimensionConstructible and HilbertSpace.
> Yes, that would do it.
> Matthias
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