On Range Inclusion of Polynomials Applying Interval Arithmetic

Shinya Miyajima, Masahide Kashiwagi

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)725-731
    Number of pages7
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE87-A
    Issue number3
    Publication statusPublished - 2004 Mar

    Fingerprint

    Interval Arithmetic
    Inclusion
    Polynomials
    Polynomial
    Range of data
    Numerical Examples

    Keywords

    • Interval arithmetic
    • Numerical computation with guaranteed accuracy
    • Polynomial
    • Range inclusion

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Hardware and Architecture
    • Information Systems

    Cite this

    On Range Inclusion of Polynomials Applying Interval Arithmetic. / Miyajima, Shinya; Kashiwagi, Masahide.

    In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E87-A, No. 3, 03.2004, p. 725-731.

    Research output: Contribution to journalArticle

    @article{ea6388da787b4c22ace020cc0fc6924c,
    title = "On Range Inclusion of Polynomials Applying Interval Arithmetic",
    abstract = "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.",
    keywords = "Interval arithmetic, Numerical computation with guaranteed accuracy, Polynomial, Range inclusion",
    author = "Shinya Miyajima and Masahide Kashiwagi",
    year = "2004",
    month = "3",
    language = "English",
    volume = "E87-A",
    pages = "725--731",
    journal = "IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences",
    issn = "0916-8508",
    publisher = "Maruzen Co., Ltd/Maruzen Kabushikikaisha",
    number = "3",

    }

    TY - JOUR

    T1 - On Range Inclusion of Polynomials Applying Interval Arithmetic

    AU - Miyajima, Shinya

    AU - Kashiwagi, Masahide

    PY - 2004/3

    Y1 - 2004/3

    N2 - 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.

    AB - 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.

    KW - Interval arithmetic

    KW - Numerical computation with guaranteed accuracy

    KW - Polynomial

    KW - Range inclusion

    UR - http://www.scopus.com/inward/record.url?scp=1842586060&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=1842586060&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:1842586060

    VL - E87-A

    SP - 725

    EP - 731

    JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

    JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

    SN - 0916-8508

    IS - 3

    ER -