EigenPower< VECTOR > Class Template Reference
[Linear solver classes]

Inheritance diagram for EigenPower< VECTOR >:

Classes
struct	AdditionalData
Public Member Functions
	EigenPower (SolverControl &cn, VectorMemory< VECTOR > &mem, const AdditionalData &data=AdditionalData())
virtual	~EigenPower ()
template<class MATRIX >
void	solve (double &value, const MATRIX &A, VECTOR &x)
Protected Attributes
AdditionalData	additional_data

Detailed Description

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

Power method (von Mises) for eigenvalue computations.

This method determines the largest eigenvalue of a matrix by applying increasing powers of this matrix to a vector. If there is an eigenvalue $l$ with dominant absolute value, the iteration vectors will become aligned to its eigenspace and $Ax = lx$ .

A shift parameter allows to shift the spectrum, so it is possible to compute the smallest eigenvalue, too.

Convergence of this method is known to be slow.

Author:: Guido Kanschat, 2000

Constructor & Destructor Documentation

template<class VECTOR >

EigenPower< VECTOR >::EigenPower	(	SolverControl &	cn,
		VectorMemory< VECTOR > &	mem,
		const AdditionalData &	data = `AdditionalData()`
	)			`[inline]`

Constructor.

template<class VECTOR >

EigenPower< VECTOR >::~EigenPower ( ) [inline, virtual]

Virtual destructor.

Member Function Documentation

template<class VECTOR >

template<class MATRIX >

void EigenPower< VECTOR >::solve	(	double &	value,
		const MATRIX &	A,
		VECTOR &	x
	)			`[inline]`

Power method. 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.

References EigenPower< VECTOR >::additional_data, Assert, SolverControl::check(), Solver< VECTOR >::control(), deallog, SolverControl::iterate, Solver< VECTOR >::memory, LogStream::pop(), LogStream::push(), EigenPower< VECTOR >::AdditionalData::shift, and SolverControl::success.