com.numericalmethod.suanshu.matrix.doubles.factorization.eigen
Class InverseIteration

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.InverseIteration

public class InverseIteration
extends java.lang.Object

Inverse iteration is an iterative eigenvalue algorithm. It finds an approximate eigenvector when an approximation to an eigenvalue is already known. Inverse iteration does not apply when λ is the exact eigenvalue because (A - λI) is singular.

See Also:

• Wikipedia: Inverse iteration
• "G. H. Golub, C. F. van Loan, "Section 2.4.1," Matrix Computations, 3rd edition."
• COMPUTING AN EIGENVECTOR WITH INVERSE ITERATION, ILSE C. F. IPSEN.

Nested Class Summary

static interface

InverseIteration.StoppingCriterion This interface defines the convergence criterion.

Constructor Summary

InverseIteration(Matrix A, double lambda)
Construct an instance of InverseIteration to find the corresponding eigenvector.

InverseIteration(Matrix A, double lambda, InverseIteration.StoppingCriterion criterion)
Construct an instance of InverseIteration to find the corresponding eigenvector.

Method Summary

Vector	getEigenVector() Get an eigenvector.
Vector	getEigenVector(Vector v0, int maxIterations) Get an eigenvector from an initial guess.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

InverseIteration

public InverseIteration(Matrix A,
                        double lambda,
                        InverseIteration.StoppingCriterion criterion)

Construct an instance of InverseIteration to find the corresponding eigenvector.

Parameters:

A - a matrix

lambda - an eigenvalue

criterion - a convergence criterion

InverseIteration

public InverseIteration(Matrix A,
                        double lambda)

Construct an instance of InverseIteration to find the corresponding eigenvector.

Parameters:

A - a matrix

lambda - an eigenvalue

Method Detail

getEigenVector

public Vector getEigenVector(Vector v0,
                             int maxIterations)

Get an eigenvector from an initial guess.

Parameters:

v0 - an initial guess of eigenvector

maxIterations - the maximum number of iterations, e.g., 10

Returns:

an approximate eigenvector

getEigenVector

public Vector getEigenVector()

Get an eigenvector.

Returns:

an approximate eigenvector