The algebraic eigenvalue problem
The algebraic eigenvalue problem
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
Robust and efficient evaluation of functionals on parametric surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
ACM Transactions on Mathematical Software (TOMS)
Keynote lecture: shape interrogation
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Accuracy and semantics in shape-interrogation applications
Graphical Models - Solid modeling theory and applications
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Surface interrogation and intersection depend crucially on good root-finding algorithms, which in turn depend on accurate polynomial evaluation. Conventional algorithms for evaluation typically encounter difficulties near multiple roots, or roots that are very close, and this may lead to gross errors in the geometric computation, or even catastrophic failure. In this paper we study the cost and accuracy of several approaches to polynomial evaluation, explaining the reasons for non-convergence of certain methods, and supporting our subsequent conclusions with the results of benchmarking experiments.