Title:  Mechanism of Cancellation Errors in Multivariate
          Hensel Construction with Floating-point Numbers

  Author: Tateaki Sasaki (*)  and  Mutsuko Sasaki (**)

     (*)  Institute of Mathematics, University of Tsukuba
               Tsukuba-shi, Ibaraki 305, Japan
     (**) Institute of Physical and Chemical Research
               Wako-shi, Saitama 351, Japan 

 In ISSAC'98, Sasaki and Yamaguchi showed that multivariate Hensel
construction  with floating-point  numbers causes  large numerical
errors  if the expansion point  is chosen  near  a singular point.
However, their analysis  was based  on Cauchy-Hadamard's  theorem,
and the mechanism of term cancellation was unclear. In this paper,
we clarify how terms cancel in the process of Hensel construction.
First, we investigate  Moses-Yun's interpolation polynomials which
play  an essential role  in the construction, and  clarify several
important properties  of them.  Then, we  clarify four  mechanisms
of term cancellation.  Second, we investigate the numerical errors
caused  by the term cancellations in two cases;  the case that the
expansion point is  near a singular point, and  the case  that the
expansion point  is far from the singular points.  The latter case
is reduced  to the former case by a scale transformation.  We show
that, in both cases, there  may  occur  large cancellation  errors
depending on the type of singularity.