@PublicationReference(author="Wikipedia", title="Power iteration", type=WebPage, year=2009, url="http://en.wikipedia.org/wiki/Power_iteration") public class EigenvectorPowerIteration extends AbstractCloneableSerializable
Modifier and Type  Field and Description 

static int 
DEFAULT_MAXIMUM_ITERATIONS
Default maximum iterations for power iteration, 100.

static double 
DEFAULT_STOPPING_THRESHOLD
Default stopping threshold for power iteration, 1.0E5.

Constructor and Description 

EigenvectorPowerIteration()
Creates a new instance of EigenvectorPowerIteration.

Modifier and Type  Method and Description 

static double 
estimateEigenvalue(Matrix A,
Vector v)
Finds the eigenvalue associated with the given Matrix and eigenvector.

static Vector 
estimateEigenvector(Vector initial,
Matrix A,
double stoppingThreshold,
int maxIterations)
Estimates the eigenvector corresponding to the largest magnitude
eigenvalue.

static java.util.ArrayList<Vector> 
estimateEigenvectors(Matrix A,
int numEigenvectors)
Estimates the top eigenvectors of the given matrix using the power
iteration algorithm.

static java.util.ArrayList<Vector> 
estimateEigenvectors(Matrix A,
int numEigenvectors,
double stoppingThreshold,
int maxIterations)
Estimates the top eigenvectors of the given matrix using the power
iteration algorithm.

clone
public static final double DEFAULT_STOPPING_THRESHOLD
public static final int DEFAULT_MAXIMUM_ITERATIONS
public EigenvectorPowerIteration()
public static java.util.ArrayList<Vector> estimateEigenvectors(Matrix A, int numEigenvectors)
A
 The matrix to estimate the eigenvectors for. It must be symmetric.
It will be modified by the algorithm.numEigenvectors
 The number of eigenvectors to compute.public static java.util.ArrayList<Vector> estimateEigenvectors(Matrix A, int numEigenvectors, double stoppingThreshold, int maxIterations)
A
 The matrix to estimate the eigenvectors for. It must be symmetric.
It will be modified by the algorithm.numEigenvectors
 The number of eigenvectors to compute.stoppingThreshold
 The stopping threshold for the power iteration algorithm. The
algorithm will stop its computation of an eigenvector when themaxIterations
 The maximum number of iterations for the power iteration algorithm.public static Vector estimateEigenvector(Vector initial, Matrix A, double stoppingThreshold, int maxIterations)
initial
 Initial estimate of the eigenvector. This is generally a uniform
(constant nonzero) Vector.A
 The matrix to estimate the eigenvectors for. It must be symmetric.
It will be modified by the algorithm.stoppingThreshold
 The stopping threshold for the power iteration algorithm. The
algorithm will stop its computation of an eigenvector when themaxIterations
 The maximum number of iterations for the power iteration algorithm.public static double estimateEigenvalue(Matrix A, Vector v)
A
 Matrix to estimate the eigenvalue of. May have negative, repeated,
positive, or zero eigenvaluesv
 Eigenvector associated with the unknown eigenvalue