### Abstract

Interval arithmetic is able to be applied in the case that we evaluate the ranges of polynomials. When we evaluate the ranges of polynomials by applying the interval arithmetic, the problem that interval widths of the ranges increase extremely exists. Horner's method is widely known as the evaluating method which mitigates this problem. The purpose of this paper is to propose the new methods which are able to mitigate this problem more efficiently than the Horner's method. And in this paper, we show and compare the efficiencies of the each new method by the results of some numerical examples.

Original language | English |
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Pages (from-to) | 254-261 |

Number of pages | 8 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2907 |

Publication status | Published - 2004 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

**On Range Evaluation of Polynomials by Applying Interval Arithmetic.** / Miyajima, Shinya; Kashiwagi, Masahide.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On Range Evaluation of Polynomials by Applying Interval Arithmetic

AU - Miyajima, Shinya

AU - Kashiwagi, Masahide

PY - 2004

Y1 - 2004

N2 - Interval arithmetic is able to be applied in the case that we evaluate the ranges of polynomials. When we evaluate the ranges of polynomials by applying the interval arithmetic, the problem that interval widths of the ranges increase extremely exists. Horner's method is widely known as the evaluating method which mitigates this problem. The purpose of this paper is to propose the new methods which are able to mitigate this problem more efficiently than the Horner's method. And in this paper, we show and compare the efficiencies of the each new method by the results of some numerical examples.

AB - Interval arithmetic is able to be applied in the case that we evaluate the ranges of polynomials. When we evaluate the ranges of polynomials by applying the interval arithmetic, the problem that interval widths of the ranges increase extremely exists. Horner's method is widely known as the evaluating method which mitigates this problem. The purpose of this paper is to propose the new methods which are able to mitigate this problem more efficiently than the Horner's method. And in this paper, we show and compare the efficiencies of the each new method by the results of some numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=35048877824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35048877824&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:35048877824

VL - 2907

SP - 254

EP - 261

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -