Class HessenbergDeflationSearch


  • public class HessenbergDeflationSearch
    extends Object
    Given a Hessenberg matrix, this class searches the largest unreduced Hessenberg sub-matrix.
    • Constructor Detail

      • HessenbergDeflationSearch

        public HessenbergDeflationSearch​(boolean setNegligibleEntriesToZeros,
                                         double epsilon)
      • HessenbergDeflationSearch

        public HessenbergDeflationSearch​(DeflationCriterion deflationCriterion,
                                         boolean setNegligibleEntriesToZeros,
                                         double epsilon)
    • Method Detail

      • backSearch

        public Deflation backSearch​(Matrix H)
        Finds H22 such that H22 is the largest unreduced Hessenberg sub-matrix, and H33 is upper quasi-triangular. For performance reason, this implementation has a side effect: the method modifies the input H by rounding the negligible sub-diagonal elements to 0. H22 an unreduced Hessenberg in Algorithm 7.5.2 has the dimension \((l_r-u_l+1) \times (l_r-u_l+1)\). We try to minimize \(u_l\) (hence maximize the H22 dimension). H33 an upper quasi-triangular in Algorithm 7.5.2 has dimension \((n-l_r) \times (n-l_r)\). We try to minimize \(l_r\) (hence maximize the H33 dimension).
        Parameters:
        H - a Hessenberg matrix
        Returns:
        deflation information; null if no deflation is found, hence the input matrix is already quasi-triangular