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

Interface Hessenberg.DeflationCriterion

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

Hessenberg.DefaultDeflationCriterion

Enclosing class:

Hessenberg

public static interface Hessenberg.DeflationCriterion
extends java.io.Serializable

Deflation of an upper Hessenberg matrix splits it into multiple smaller upper Hessenberg matrices when the sub-diagonal entries are sufficiently small. For example, suppose \[ H = \begin{bmatrix} 1 & 2 & 3 & 4 & \\ 5 & 6 & 7 & 8 & \\ 0 & 9 & 10 & 11 & \\ 0 & 0 & 12 & 13 & \end{bmatrix} \] We can split H into H₁ and H₂, so that \[ H_1 = \begin{bmatrix} 1 & 2 \\ 5 & 6 \\ \end{bmatrix} \] \[ H_2 = \begin{bmatrix} 10 & 11 \\ 12 & 13 \\ \end{bmatrix} \]

See Also:

"Golub and van Loan, Section 7.5.1."

Method Summary

Modifier and Type	Method and Description
boolean	isNegligible(Matrix H, int i, int j, double epsilon) Check whether a sub-diagonal element is sufficiently small.

Method Detail

isNegligible

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

Check whether a sub-diagonal element is sufficiently small.

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 is H[i,j] is deemed small enough