Class SturmCount


  • public class SturmCount
    extends Object
    Computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - σ I = LDLT. 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 Detail

      • SturmCount

        public SturmCount​(LDDecomposition LDLt,
                          int twistIndex)
        Creates an instance for computing the Sturm count of a given robust representation (T - σ I = LDLT).
        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