Class HessenbergDeflationSearch
- java.lang.Object
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- dev.nm.algebra.linear.matrix.doubles.factorization.eigen.qr.HessenbergDeflationSearch
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public class HessenbergDeflationSearch extends Object
Given a Hessenberg matrix, this class searches the largest unreduced Hessenberg sub-matrix.
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Constructor Summary
Constructors Constructor Description HessenbergDeflationSearch(boolean setNegligibleEntriesToZeros, double epsilon)
HessenbergDeflationSearch(DeflationCriterion deflationCriterion, boolean setNegligibleEntriesToZeros, double epsilon)
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description Deflation
backSearch(Matrix H)
Finds H22 such that H22 is the largest unreduced Hessenberg sub-matrix, and H33 is upper quasi-triangular.
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Constructor Detail
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HessenbergDeflationSearch
public HessenbergDeflationSearch(boolean setNegligibleEntriesToZeros, double epsilon)
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HessenbergDeflationSearch
public HessenbergDeflationSearch(DeflationCriterion deflationCriterion, boolean setNegligibleEntriesToZeros, double epsilon)
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Method Detail
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backSearch
public Deflation backSearch(Matrix H)
Finds H22 such that H22 is the largest unreduced Hessenberg sub-matrix, and H33 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 H22 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 H33 dimension).- Parameters:
H
- a Hessenberg matrix- Returns:
- deflation information;
null
if no deflation is found, hence the input matrix is already quasi-triangular
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