com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.qr

Class Hessenberg.DefaultDeflationCriterion

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.qr.Hessenberg.DefaultDeflationCriterion

All Implemented Interfaces:

Hessenberg.DeflationCriterion, java.io.Serializable

Enclosing class:

Hessenberg

public static class Hessenberg.DefaultDeflationCriterion
extends java.lang.Object
implements Hessenberg.DeflationCriterion

The default deflation criterion is to use eq. 7.5.2 in Golub and van Loan: H[i,j] is negligible when

| H[i,j] | < tol * (| H[i-1,j] | + | H[i,j+1] |)

or, when

| H[i-1,j] | + | H[i,j+1] | == 0

and to use eq. 2.26 in Matrix Algorithms, Volume II by Steward G. W.

| H[i,j] | < tol * ||A||F

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
DefaultDeflationCriterion() Construct the default deflation criterion.
DefaultDeflationCriterion(double threshold) Construct the default deflation criterion.

Method Summary

Modifier and Type	Method and Description
boolean	isNegligible(Matrix H, int i, int j, double epsilon) Check if H[i,j] is negligible by Steward's deflation criterion.

Methods inherited from class java.lang.Object

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

Constructor Detail

DefaultDeflationCriterion

public DefaultDeflationCriterion(double threshold)

Construct the default deflation criterion.

Parameters:

threshold - the tolerance in Steward's deflation criterion

DefaultDeflationCriterion

public DefaultDeflationCriterion()

Construct the default deflation criterion.

Method Detail

isNegligible

public boolean isNegligible(Matrix H,
                            int i,
                            int j,
                            double epsilon)

Check if H[i,j] is negligible by Steward's deflation criterion.

Specified by:

isNegligible in interface Hessenberg.DeflationCriterion

Parameters:

H - a matrix

i - a row index

j - a column index

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true if

| H[i,j] | < tol * (| H[i-1,j] | + | H[i,j+1] |)