com.numericalmethod.suanshu.matrix.doubles.factorization.eigen
Interface Hessenberg.DeflationCriterion

All Known Implementing Classes:

Hessenberg.DefaultDeflationCriterion

Enclosing class:

Hessenberg

public static interface Hessenberg.DeflationCriterion

User implements this class to decide whether to split an upper Hessenberg into multiple smaller upper Hessenberg when the sub-diagonal entries are sufficiently small.

E.g., Suppose H =

 | 1 2 3 4   |
 | 5 6 7 8   |
 | 0 0 10 11 |
 | 0 0 12 13 |
 

We can split H into H1 and H2, so that

H1 =

 | 1 2 |
 | 5 6 |
 

H2 =

 | 10 11 |
 | 12 13 |
 

See Also:

"Section 7.5.1. Golub and van Loan."

Method Summary

boolean

isNegligible(Matrix H, int row, int col, double epsilon) Check whether a sub-diagonal element is sufficiently small.

Method Detail

isNegligible

boolean isNegligible(Matrix H,
                     int row,
                     int col,
                     double epsilon)

Check whether a sub-diagonal element is sufficiently small.

Parameters:

H - a matrix

row - row index

col - column index

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

Returns:

true is H[row, col] is deemed small enough