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              The International Computer Science Institute
                     is pleased to present a talk:

                   Friday, August 28, 1992  2:00 p.m.

                          PROF. J. HERZBERGER
                         Fachbereich Mathematik
                    Universitaet Oldenburg, GERMANY

           On Some Classes of Simultaneous Inclusion Methods
                          for Polynomial Zeros

           We are investigating a general model for the  construc-
      tion  of  higher-order  simultaneous  inclusion  methods for
      polynomial zeros based on fixed-point relations.   In  order
      to  calculate guaranteed bounds for the zeros we make use of
      interval operations in the definition of the iteration  for-
      mulas.  We are considering:

      (i)  a total-step approach (convenient for parallel computa-
           tion)

      (ii) a single-step approach (convenient for serial  computa-
           tion)

           As special cases many well-known  iteration methods  in
      the  literature  are  included.  For the families under con-
      sideration it is shown that their order of  convergence  can
      easily be determined.  The single-step methods are proved to
      be superior to the total-step methods with  respect  to  the
      R-order of convergence.

           The methods derived in that way  are  producing  nested
      sequences of inclusion intervals for the zeros.  If a proper
      machine interval arithmetic is used,  for  example,  with  a
      PASCAL-XSC compiler, then these bounds are guaranteed in the
      presence of round-off errors.  Besides the general treatment
      of the methods in recent literature, some new methods can be
      derived which are requiring a rather complicated analysis to
      prove their basic properties without using our model.

           Some examples are given showing how  this  model  works
      when applied to concrete methods.


        This talk will be held in the Main Lecture Hall at ICSI.
          1947 Center Street, Sixth Floor, Berkeley, CA 94704
       (On Center between Milvia and Martin Luther King Jr. Way)


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