This paper is concerned with certifying that a given point is near an exact root of an
overdetermined or singular polynomial system with rational coefficients. The difficulty lies in …

In this paper we present two efficient methods for reconstructing a rational number from
several residue-modulus pairs, some of which may be incorrect. One method is a natural …

An iterative refinement approach is taken to rational linear system solving. Such methods
produce, for each entry of the solution vector, a rational approximation with denominator a …

The problem of computing the greatest common divisor (GCD) of multivariate polynomials,
as one of the most important tasks of computer algebra and symbolic computation in more …

Hybrid systems with non-polynomial components are widely used in modeling safety critical
applications. Due to the complexity arisen from the non-polynomial expression, safety …

Linear algebra, together with polynomial arithmetic, is the foundation of computer algebra.
The algorithms have improved over the last 20 years, and the current state of the art …

摘要研究采用有误差的数值计算来获得无误差的准确值具有重要的理论价值和应用价值.
这种通过**似的数值方法获得准确结果的计算被称为零误差计算. 本文首先指出 …