eigensolver::InexactInv< F > Class Template Reference

#include <inexactInv.hh>

Inheritance diagram for eigensolver::InexactInv< F >:

Public Member Functions
	InexactInv (concepts::Operator< F > &A, concepts::Operator< F > &B, const concepts::Vector< F > &EFguess, const Real innerTol=0.5, const uint innerMax=100, const Real outerTol=1e-6, const uint outerMax=100)
virtual const concepts::Array< F > &	getEV ()
virtual const concepts::Array< concepts::Vector< F > * > &	getEF ()
virtual uint	iterations () const
	Returns the number of iterations.
virtual uint	converged () const
	Returns the number of converged eigen pairs.

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Detailed Description

template<typename F>
class eigensolver::InexactInv< F >

Inexact inverse iteration to solve a generalized Eigen value problem. The problem to be solved is . This algorithm uses the inexact solution of a linear system to converge to the first Eigen pair of the Eigen problem.

The class is templated on the value type but only the real part works.

Author

Philipp Frauenfelder, 2003

Test:

test::GolubExample

test::GolubExampleSum

test::MaxwellTransmissionEVP

See also

Gene H. Golub and Qiang Ye, Inexact inverse iteration for generalized Eigenvalue problems, BIT Vol. 40, No. 4 (2000), 671-684.

Definition at line 36 of file inexactInv.hh.

Constructor & Destructor Documentation

InexactInv()

template<typename F >

eigensolver::InexactInv< F >::InexactInv	(	concepts::Operator< F > &	A,
		concepts::Operator< F > &	B,
		const concepts::Vector< F > &	EFguess,
		const Real	innerTol = 0.5,
		const uint	innerMax = 100,
		const Real	outerTol = 1e-6,
		const uint	outerMax = 100
	)

Constructor. The relative tolerance for the innner iteration can be kept fairly high. In fact, where . Best results are achieved for only slightly larger than .

Parameters

A	A
B	B
EFguess	Initial value for the Eigen function
innerTol	Relative tolerance for the inner iteration (solution of the linear system)
innerMax	Maximal number of iterations for the inner iteration
outerTol	Tolerance for the outer iteration (residual of the Eigen function)
outerMax	Maximal number of outer iterations

Member Function Documentation

converged()

template<typename F >

virtual uint eigensolver::InexactInv< F >::converged ( ) const

inlinevirtual

Returns the number of converged eigen pairs.

Implements eigensolver::EigenSolver< F >.

Definition at line 67 of file inexactInv.hh.

getEF()

template<typename F >

virtual const concepts::Array< concepts::Vector< F > * > & eigensolver::InexactInv< F >::getEF ( )

inlinevirtual

Implements eigensolver::EigenSolver< F >.

Definition at line 62 of file inexactInv.hh.

getEV()

template<typename F >

virtual const concepts::Array< F > & eigensolver::InexactInv< F >::getEV ( )

inlinevirtual

Returns an array with the eigen values

Deprecated:

: this interface requires that the returned array must be hold as a member variable of the class. (use std::auto_pointer or similar)

Implements eigensolver::EigenSolver< F >.

Definition at line 59 of file inexactInv.hh.

info()

template<typename F >

virtual std::ostream & eigensolver::InexactInv< F >::info ( std::ostream &  os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from eigensolver::EigenSolver< F >.

iterations()

template<typename F >

virtual uint eigensolver::InexactInv< F >::iterations ( ) const

inlinevirtual

Returns the number of iterations.

Implements eigensolver::EigenSolver< F >.

Definition at line 66 of file inexactInv.hh.

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

• eigensolver/inexactInv.hh