MathTL::Preconditioner< VECTOR > Class Template Reference

#include <preconditioner.h>

Inheritance diagram for MathTL::Preconditioner< VECTOR >:

List of all members.

Public Types
typedef VECTOR::size_type	size_type
Public Member Functions
virtual	~Preconditioner ()=0
virtual const size_type	row_dimension () const =0
const size_type	column_dimension () const
virtual void	apply (const VECTOR &x, VECTOR &Px) const =0
virtual void	apply_preconditioner (const VECTOR &Px, VECTOR &x) const =0

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Detailed Description

template<class VECTOR>
class MathTL::Preconditioner< VECTOR >

Abstract base class for preconditioners P of (finite) linear systems Ax=b.

In applications, the class will be used to model both preconditioning

• from the left (solve P^{-1}Ax=P^{-1}b instead of Ax=b), and
• from the right (solve AQ^{-1}y=b and x=Q^{-1}y instead of Ax=b)

Preconditioners P behave like square matrices, the solution of linear systems Px=y should be cheap.

References:

[B] M. Benzi: Preconditioning Techniques for Large Linear Systems: A Survey J. Comput. Phys. 182(2002), 418-477

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Member Typedef Documentation

template<class VECTOR >

typedef VECTOR::size_type MathTL::Preconditioner< VECTOR >::size_type

type of indices and size type (cf. STL containers)

Reimplemented in MathTL::JacobiPreconditioner< MATRIX, VECTOR >, and MathTL::IdentityPreconditioner< MATRIX, VECTOR >.

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Constructor & Destructor Documentation

template<class VECTOR >

MathTL::Preconditioner< VECTOR >::~Preconditioner

(

)

[pure virtual]

purely virtual destructor

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Member Function Documentation

template<class VECTOR >

virtual void MathTL::Preconditioner< VECTOR >::apply	(	const VECTOR &	x,
		VECTOR &	Px
	)		const [pure virtual]

apply P, i.e., reverse the preconditioning

Implemented in MathTL::JacobiPreconditioner< MATRIX, VECTOR >, and MathTL::IdentityPreconditioner< MATRIX, VECTOR >.

template<class VECTOR >

virtual void MathTL::Preconditioner< VECTOR >::apply_preconditioner	(	const VECTOR &	Px,
		VECTOR &	x
	)		const [pure virtual]

apply P^{-1}, i.e., perform the preconditioning

Implemented in MathTL::JacobiPreconditioner< MATRIX, VECTOR >, and MathTL::IdentityPreconditioner< MATRIX, VECTOR >.

template<class VECTOR >

const size_type MathTL::Preconditioner< VECTOR >::column_dimension

(

)

const [inline]

column dimension (== row dimension)

template<class VECTOR >

virtual const size_type MathTL::Preconditioner< VECTOR >::row_dimension

(

)

const [pure virtual]

row dimension

Implemented in MathTL::JacobiPreconditioner< MATRIX, VECTOR >, and MathTL::IdentityPreconditioner< MATRIX, VECTOR >.

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The documentation for this class was generated from the following files:

• numerics/preconditioner.h
• numerics/preconditioner.cpp