Reference documentation for deal.II version 8.1.0
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EigenInverse< VECTOR > Class Template Reference

#include <eigen.h>

Inheritance diagram for EigenInverse< VECTOR >:
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Classes

struct  AdditionalData
 

Public Types

typedef types::global_dof_index size_type
 

Public Member Functions

 EigenInverse (SolverControl &cn, VectorMemory< VECTOR > &mem, const AdditionalData &data=AdditionalData())
 
virtual ~EigenInverse ()
 
template<class MATRIX >
void solve (double &value, const MATRIX &A, VECTOR &x)
 

Protected Attributes

AdditionalData additional_data
 

Additional Inherited Members

- Private Member Functions inherited from Solver< VECTOR >
 Solver (SolverControl &solver_control, VectorMemory< VECTOR > &vector_memory)
 
 Solver (SolverControl &solver_control)
 
SolverControlcontrol () const
 
- Private Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
- Private Attributes inherited from Solver< VECTOR >
GrowingVectorMemory< VECTOR > static_vector_memory
 
SolverControlcntrl
 
VectorMemory< VECTOR > & memory
 

Detailed Description

template<class VECTOR = Vector<double>>
class EigenInverse< VECTOR >

Inverse iteration (Wieland) for eigenvalue computations.

This class implements an adaptive version of the inverse iteration by Wieland.

There are two choices for the stopping criterion: by default, the norm of the residual $A x - l x$ is computed. Since this might not converge to zero for non-symmetric matrices with non-trivial Jordan blocks, it can be replaced by checking the difference of successive eigenvalues. Use AdditionalData::use_residual for switching this option.

Usually, the initial guess entering this method is updated after each step, replacing it with the new approximation of the eigenvalue. Using a parameter AdditionalData::relaxation between 0 and 1, this update can be damped. With relaxation parameter 0, no update is performed. This damping allows for slower adaption of the shift value to make sure that the method converges to the eigenvalue closest to the initial guess. This can be aided by the parameter AdditionalData::start_adaption, which indicates the first iteration step in which the shift value should be adapted.

Author
Guido Kanschat, 2000, 2003

Definition at line 149 of file eigen.h.

Member Typedef Documentation

template<class VECTOR = Vector<double>>
typedef types::global_dof_index EigenInverse< VECTOR >::size_type

Declare type of container size.

Definition at line 155 of file eigen.h.

Constructor & Destructor Documentation

template<class VECTOR >
EigenInverse< VECTOR >::EigenInverse ( SolverControl cn,
VectorMemory< VECTOR > &  mem,
const AdditionalData data = AdditionalData() 
)

Constructor.

Definition at line 329 of file eigen.h.

template<class VECTOR >
EigenInverse< VECTOR >::~EigenInverse ( )
virtual

Virtual destructor.

Definition at line 340 of file eigen.h.

Member Function Documentation

template<class VECTOR >
template<class MATRIX >
void EigenInverse< VECTOR >::solve ( double value,
const MATRIX A,
VECTOR &  x 
)

Inverse method. value is the start guess for the eigenvalue and x is the (not necessarily normalized, but nonzero) start vector for the power method. After the iteration, value is the approximated eigenvalue and x is the corresponding eigenvector, normalized with respect to the l2-norm.

Definition at line 348 of file eigen.h.

Member Data Documentation

template<class VECTOR = Vector<double>>
AdditionalData EigenInverse< VECTOR >::additional_data
protected

Flags for execution.

Definition at line 228 of file eigen.h.


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