On Range Inclusion of Polynomials Applying Interval Arithmetic

Shinya MIYAJIMA  Masahide KASHIWAGI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.3   pp.725-731
Publication Date: 2004/03/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
Keyword: 
numerical computation with guaranteed accuracy,  interval arithmetic,  range inclusion,  polynomial,  

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Summary: 
Interval arithmetic is able to be applied when we include the ranges of various functions. When we include them applying the interval arithmetic, the serious problem that the widths of the range inclusions increase extremely exists. In range inclusion of polynomials particularly, Horner's method and Alefeld's method are well known as the conventional methods 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 conventional methods. And in this paper, we show and compare the efficiencies of the new methods by some numerical examples.