### Abstract

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.

Original language | English (US) |
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Title of host publication | ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation |

Pages | 387-388 |

Number of pages | 2 |

DOIs | |

State | Published - Dec 1 2009 |

Event | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of Duration: Jul 28 2009 → Jul 31 2009 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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### Other

Other | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 7/28/09 → 7/31/09 |

### Fingerprint

### Keywords

- Adaptive complexity analysis
- Exact numerical computation
- Explicitization problems
- Numerical algebraic computation
- Numerical computational geometry
- Zero bounds

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation*(pp. 387-388). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1576702.1576757