## Estimation of Cancellation Errors in Multivariate Hensel Construction with Floating-Point Numbers

*Kosaku Nagasaka*

`nagasaka@math.tsukuba.ac.jp`

see below(no spaces)

**Doctral Program in Math., Univ. of Tsukuba**

Tsukuba-shi Ibaraki, 305-8571, JAPAN

Japan

### Abstract

Multivariate Hensel construction with floating-point numbers
often cause large cancellation errors which are errors due to
cancellation of almost the same numbers. Sasaki and Yamaguchi
[SY98] showed that multivariate Hensel construction causes
large cancellation errors if the expansion point is chosen
near a singular point, and Sasaki [Sas00] studied four
echanisms of term cancellations near a singular point.
However, an analysis of cancellation errors, if the expansion
point is chosen randomly, has never been studied. Moreover,
in practical computations, it is better that we employ the
lowest working precision which is almost enough to that
a result of the Hensel construction includes required
significant digits, since a higher precision takes more
computation times. In this paper, we investigate cancellation
errors without an assumption that the expansion point is
chosen near a singular point, and estimate a precision which
is almost enough.
[SY98] : T. Sasaki and S. Yamaguchi, An Analysis of
Cancellation Error in Multivariate Hensel
Construction with Floting-point Number Arithmetic,
ISSAC'98.
[Sas00] : T. Sasaki, Mechanism of cancellation errors in
multivariate Hensel construction with floting-point
numbers, Preprint of Univ. Tsukuba.

© ATCM, Inc. 2001.