On the Correctness of Parallel Bisection in Floating

  title={On the Correctness of Parallel Bisection in Floating},
  author={PointJames W. Demmel},
  • PointJames W. Demmel
  • Published 1994
Bisection is an easily parallelizable method for nding the eigenvalues of real symmetric tridiagonal matrices, or more generally symmetric acyclic matrices. It requires a function Count(x) which counts the number of eigenvalues less than x. In exact arithmetic Count(x) is an increasing function of x, but this is not necessarily the case with roundo . Our rst result is that as long as the oating point arithmetic is monotonic, the computed function Count(x) implemented appropriately will also be… CONTINUE READING