math::BanachSpace< N, Vector, Scalar > Struct Template Reference
[Concepts]

Concept BanachSpace. More...

#include <vector_concepts.hpp>

Inheritance diagram for math::BanachSpace< N, Vector, Scalar >:
math::Norm< N, Vector, Scalar > math::VectorSpace< Vector, Scalar > math::HilbertSpace< I, Vector, Scalar, N >

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:
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