dev.nm.algebra.linear.matrix.doubles.factorization.eigen.qr

Class HessenbergDeflationSearch

java.lang.Object

dev.nm.algebra.linear.matrix.doubles.factorization.eigen.qr.HessenbergDeflationSearch

public class HessenbergDeflationSearch
extends Object

Given a Hessenberg matrix, this class searches the largest unreduced Hessenberg sub-matrix.

Constructor Summary

Constructors

Constructor and Description
HessenbergDeflationSearch(boolean setNegligibleEntriesToZeros, double epsilon)
HessenbergDeflationSearch(DeflationCriterion deflationCriterion, boolean setNegligibleEntriesToZeros, double epsilon)

Method Summary

Modifier and Type	Method and Description
Deflation	backSearch(Matrix H) Finds \(H_{22}\) such that \(H_{22}\) is the largest unreduced Hessenberg sub-matrix, and \(H_{33}\) is upper quasi-triangular.

Methods inherited from class java.lang.Object

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

Constructor Detail

HessenbergDeflationSearch

public HessenbergDeflationSearch(boolean setNegligibleEntriesToZeros,
                                 double epsilon)

HessenbergDeflationSearch

public HessenbergDeflationSearch(DeflationCriterion deflationCriterion,
                                 boolean setNegligibleEntriesToZeros,
                                 double epsilon)

Method Detail

backSearch

public Deflation backSearch(Matrix H)

Finds \(H_{22}\) such that \(H_{22}\) is the largest unreduced Hessenberg sub-matrix, and \(H_{33}\) is upper quasi-triangular. For performance reason, this implementation has a side effect: the method modifies the input H by rounding the negligible sub-diagonal elements to 0. H22 an unreduced Hessenberg in Algorithm 7.5.2 has the dimension \((l_r-u_l+1) \times (l_r-u_l+1)\). We try to minimize \(u_l\) (hence maximize the \(H_{22}\) dimension). H33 an upper quasi-triangular in Algorithm 7.5.2 has dimension \((n-l_r) \times (n-l_r)\). We try to minimize \(l_r\) (hence maximize the \(H_{33}\) dimension).

Parameters:

H - a Hessenberg matrix

Returns:

deflation information; null if no deflation is found, hence the input matrix is already quasi-triangular

See Also:

"G. W. Steward, "Algorithm 3.3," Matrix Algorithms, Volume II"