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

Class SturmCount

java.lang.Object

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

public class SturmCount
extends Object

Computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal \(T - \sigma I = LDL^{\mathsf T}\). This implementation works directly on the factors without forming the tridiagonal matrix T. The Sturm count is also the number of eigenvalues of T less than σ.

See Also:

• "Marques, Osni A., Riedy E. Jason, and Vomel Christof, "LAPACK working note 172: Benefits of IEEE-754 features in modern symmetric tridiagonal eigensolvers", Technical Report UCB// CSD-05-1414, 2005."
• "Dhillon, Inderjit S. and Parlett, Beresford N., "Orthogonal eigenvectors and relative gaps", SIAM Journal on Matrix Analysis and Applications, 2004, Vol. 25, pp. 858-899."

Constructor Summary

Constructors

Constructor and Description
SturmCount(LDDecomposition LDLt, int twistIndex) Creates an instance for computing the Sturm count of a given robust representation (\(T - \sigma I = LDL^{\mathsf T}\)).

Method Summary

Modifier and Type	Method and Description
int	count(double sigma) Computes the Sturm count.

Methods inherited from class java.lang.Object

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

Constructor Detail

SturmCount

public SturmCount(LDDecomposition LDLt,
                  int twistIndex)

Creates an instance for computing the Sturm count of a given robust representation (\(T - \sigma I = LDL^{\mathsf T}\)).

Parameters:

LDLt - the robust representation of T

twistIndex - the twist index for the twisted factorization

Method Detail

count

public int count(double sigma)

Computes the Sturm count.

Parameters:

sigma - the new shift σ

Returns:

the Sturm count