Approximate Square-free Decomposition and Root-finding of III-conditioned Algebraic Equations

• Item type: JInfP(1)
• 公開日: 1989-08-25
• タイトル: Approximate Square-free Decomposition and Root-finding of III-conditioned Algebraic Equations
• タイトル / 言語: en
• タイトル: Approximate Square-free Decomposition and Root-finding of III-conditioned Algebraic Equations
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_6501
• 資源タイプ: journal article
• 著者所属: The Institute of Physical and Chemical Research
• 著者所属: Faculty of Engineering Ehime University
• 著者所属(英): en
• 著者所属(英): The Institute of Physical and Chemical Research
• 著者所属(英): en
• 著者所属(英): Faculty of Engineering, Ehime University
• 著者名: Tateaki, Sasaki; Matu-TarowNoda
• 著者名(英): Tateaki, Sasaki; Matu-Tarow, Noda
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: The exact square-free decomposition is generalized to polynomials with coefficients of floating-point numbers and an algorithm ofヲﾀapproximate square-free decomposition is presented. Given a polynomial P(x)and a small positive numbeヲﾌ 0<ヲﾆlt;<1 the decomposition algorithm calculates polynomials Q_1 Q_2 . . . Q_l such that P(x)=Q_l(x)Q^2_2(x)...Q^l_l(x) where each root of Q_m(x)=0 is approximately equal to m multiple root or the average vdue of m close roots of P(x)= 0. The decomposition is performed by using a generalized Euclidean algorithm and the properties of approximate GCD (greatest common divisor) computed by the Euclidean algorithm is investigated by developing a theory of approximate GCD. The equations Q_i(x)=0 i=1 . . . l are much easier to solve numerically than P(x)=0. Hence we apply the approximate square-free decomposition to solving il1-conditioned algebraic equations and propose an algorithm which finds not only multiple but also close roots nicely.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: The exact square-free decomposition is generalized to polynomials with coefficients of floating-point numbers, and an algorithm ofヲﾀapproximate square-free decomposition is presented. Given a polynomial P(x)and a small positive numbeヲﾌ 0<ヲﾆlt;<1, the decomposition algorithm calculates polynomials Q_1, Q_2, . . . , Q_l such that P(x)=Q_l(x)Q^2_2(x)...Q^l_l(x),where each root of Q_m(x)=0 is approximately equal to m multiple root or the average vdue of m close roots of P(x)= 0. The decomposition is performed by using a generalized Euclidean algorithm, and the properties of approximate GCD (greatest common divisor), computed by the Euclidean algorithm, is investigated by developing a theory of approximate GCD. The equations Q_i(x)=0, i=1, . . . , l, are much easier to solve numerically than P(x)=0. Hence, we apply the approximate square-free decomposition to solving il1-conditioned algebraic equations and propose an algorithm which finds not only multiple but also close roots nicely.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA00700121
• 書誌情報: Journal of Information Processing; 巻 12, 号 2, p. 159-168, 発行日 1989-08-25
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-6652
• 出版者 / 言語: ja
• 出版者: 情報処理学会