### Abstract

Computing effective root bounds for constant algebraic expressions is a critical problem in the Exact Geometric Computation approach to robust geometric programs. Classical root bounds are often nonconstructive. Recently, various authors have proposed bounding methods which might be called constructive root bounds. For the important class of radical expressions, Burnikel et al (BFMS) have provided a constructive root bound which, in the division-free case, is an improvement over previously known bounds and is essentially tight. In the presence of division, their bound reguires a guadratic blowup in root bit-bound compared to the division-free case. We present a new constructive root bound that avoids this guadratic blowup and which is applicable to a more general class of algebraic expressions. This leads to dramatically better performance in some computations. We also give an improved version of the degree-measure bound from Mignotte and BFMS. We describe our implementation in the context of the Core Library, and report on some experimental results.

Original language | English (US) |
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Title of host publication | Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 496-505 |

Number of pages | 10 |

State | Published - 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Other

Other | 2001 Operating Section Proceedings, American Gas Association |
---|---|

Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

### Fingerprint

### Keywords

- Algorithms
- Design
- Experimentation
- Measurement
- Performance
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 496-505)

**A new constructive root bound for algebraic expressions.** / Li, Chen; Yap, Chee.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 496-505, 2001 Operating Section Proceedings, American Gas Association, Dallas, TX, United States, 4/30/01.

}

TY - GEN

T1 - A new constructive root bound for algebraic expressions

AU - Li, Chen

AU - Yap, Chee

PY - 2001

Y1 - 2001

N2 - Computing effective root bounds for constant algebraic expressions is a critical problem in the Exact Geometric Computation approach to robust geometric programs. Classical root bounds are often nonconstructive. Recently, various authors have proposed bounding methods which might be called constructive root bounds. For the important class of radical expressions, Burnikel et al (BFMS) have provided a constructive root bound which, in the division-free case, is an improvement over previously known bounds and is essentially tight. In the presence of division, their bound reguires a guadratic blowup in root bit-bound compared to the division-free case. We present a new constructive root bound that avoids this guadratic blowup and which is applicable to a more general class of algebraic expressions. This leads to dramatically better performance in some computations. We also give an improved version of the degree-measure bound from Mignotte and BFMS. We describe our implementation in the context of the Core Library, and report on some experimental results.

AB - Computing effective root bounds for constant algebraic expressions is a critical problem in the Exact Geometric Computation approach to robust geometric programs. Classical root bounds are often nonconstructive. Recently, various authors have proposed bounding methods which might be called constructive root bounds. For the important class of radical expressions, Burnikel et al (BFMS) have provided a constructive root bound which, in the division-free case, is an improvement over previously known bounds and is essentially tight. In the presence of division, their bound reguires a guadratic blowup in root bit-bound compared to the division-free case. We present a new constructive root bound that avoids this guadratic blowup and which is applicable to a more general class of algebraic expressions. This leads to dramatically better performance in some computations. We also give an improved version of the degree-measure bound from Mignotte and BFMS. We describe our implementation in the context of the Core Library, and report on some experimental results.

KW - Algorithms

KW - Design

KW - Experimentation

KW - Measurement

KW - Performance

KW - Theory

KW - Verification

UR - http://www.scopus.com/inward/record.url?scp=64049096957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=64049096957&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0898714907

SP - 496

EP - 505

BT - Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms

ER -