Concept BanachSpace.
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#include <vector_concepts.hpp>
List of all members.
Detailed Description
template<typename N, typename Vector, typename Scalar = typename Vector::value_type>
struct math::BanachSpace< N, Vector, Scalar >
Concept BanachSpace.
A Banach space is a vector space with a norm
- Parameters:
-
N | Norm functor |
Vector | The the type of a vector or a collection |
Scalar | The scalar over which the vector field is defined |
- Refinement of:
-
- Note:
- The (expressible) requirements of Banach Space are already given in Norm.
- The difference between the requirements is the completeness of the Banach space, i.e. that every Cauchy sequence w.r.t. norm(v-w) has a limit in the space. Unfortunately, completeness is never satisfied for finite precision arithmetic types.
- Another subtle difference is that Norm is not a refinement of Vectorspace
The documentation for this struct was generated from the following file:
math::BanachSpace< N, Vector, Scalar > Struct Template Reference -- MTL 4 -- Peter Gottschling and Andrew Lumsdaine
-- Gen. with
rev. 7542
on Sat Aug 11 2012 by doxygen 1.7.6.1 -- © 2010 by SimuNova UG.