Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Exact geometric computation: theory and applications
Exact geometric computation: theory and applications
A Separation Bound for Real Algebraic Expressions
Algorithmica
Reliable Implementation of Real Number Algorithms: Theory and Practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
The diamond operator: implementation of exact real algebraic numbers
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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Constructive root bounds is the fundamental technique needed to achieve guaranteed accuracy, the critical capability in Exact Geometric Computation. Known bounds are overly pessimistic in the presense of general rational input numbers. In this paper, we introduce a method which greatly improves the known bounds for k-ary rational input numbers. Since majority of input numbers in scientific and engineering applications are such numbers, this could lead to a significant speedup for a large class of applications. We apply our method to the BFMSS Bound. Implementation and experimental results based on the Core Library are reported.