dev.nm.algebra.linear.matrix.doubles.factorization.eigen.mr3

Class LDFactorizationFromRoot

java.lang.Object

dev.nm.algebra.linear.matrix.doubles.factorization.eigen.mr3.LDFactorizationFromRoot

public class LDFactorizationFromRoot
extends Object

Decomposes (T - σ I) into \(L D L^{\mathsf T}\) where T is a symmetric tridiagonal matrix, σ is a shift for this factorization, L is a unit lower triangular matrix, and D is a diagonal matrix.

See Also:

"Dhillon, Inderjit S., "A new O(n2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem", PhD thesis, 1997."

Constructor Summary

Constructors

Constructor and Description
LDFactorizationFromRoot(Vector D, Vector E, double sigma) Creates a decomposition for a symmetric tridiagonal matrix T.

Method Summary

Modifier and Type	Method and Description
Vector	D()
Vector	L()

Methods inherited from class java.lang.Object

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

Constructor Detail

LDFactorizationFromRoot

public LDFactorizationFromRoot(Vector D,
                               Vector E,
                               double sigma)

Creates a decomposition for a symmetric tridiagonal matrix T.

Parameters:

D - the diagonal entries of T

E - the off-diagonal entries of T

sigma - the shift

Method Detail

L

public Vector L()

D

public Vector D()