A course in computational algebraic number theory
A course in computational algebraic number theory
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Complete subdivision algorithms, II: isotopic meshing of singular algebraic curves
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the twenty-fifth annual symposium on Computational geometry
Topologically accurate meshing using domain subdivision techniques
Topologically accurate meshing using domain subdivision techniques
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Empirical study of an evaluation-based subdivision algorithm for complex root isolation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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Many problems in Computational Science & Engineering (CSE) are defined on the continuum. Standard algorithms for these problems are numerical and approximate. Their computational techniques include iteration, subdivision, and approximation. Such techniques are rarely seen in exact or algebraic algorithms. In this tutorial, we discuss a mode of computation called exact numerical computation (ENC) that achieves exactness through numerical approximation. Through ENC, we can naturally incorporate iteration, subdivision and approximation into the design of exact algorithms for computer algebra and computational geometry. Such algorithms are both novel and practical. This tutorial on ENC is divided into three equal parts: (a) Zero Problems (b) Explicitation Problems (c) Techniques and Complexity Analysis of Adaptivity