Analysis of Accuracy Decreasing in Polynomial Remainder Sequence with Floating-point Number Coefficients

• Item type: JInfP(1)
• 公開日: 1990-03-15
• タイトル: Analysis of Accuracy Decreasing in Polynomial Remainder Sequence with Floating-point Number Coefficients
• タイトル / 言語: en
• タイトル: Analysis of Accuracy Decreasing in Polynomial Remainder Sequence with Floating-point Number Coefficients
• 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: The Institute of Physical and Chemical Research
• 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): The Institute of Physical and Chemical Research
• 著者名: Tateaki, Sasaki; Mutsuko, Sasaki
• 著者名(英): Tateaki, Sasaki; Mutsuko, Sasaki
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Let (P_1 P_2 P_3 . . .) be the univariate polynomial remainder sequence with floating. point number coefficients. Letλ roots of P_l be close toμ roots of P_2 and let deg (P_k)=min {λ μ}. Then the accuracy of the coefficients of P_<k+i> i>0 decreases significantly. The accuracy decreasing in P_<k+1> was investigated in a previous paper. This paper almost clarifies the phenomenon of accuracy decreasing in P_<k+i> i= 1 2 . . . under the restriction that degrees of initial polynomials are not large. It is shown that if the close roots are concentrated at one point then the accuracy decreases at each calculation of P_<k+i> i> O. If the close roots are distributed around r points r> 1 which are mutually well-distant then the accuracy decreases each time the degree of remainder decreases by r. Furthermore the amount of decrease of accuracy is clarified with emphasis on the case P_2(x)z dP_1(x)/dx.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Let (P_1, P_2, P_3, . . .) be the univariate polynomial remainder sequence with floating. point number coefficients. Letλ roots of P_l be close toμ roots of P_2, and let deg (P_k)=min {λ,μ}. Then, the accuracy of the coefficients of P_<k+i>, i>0, decreases significantly. The accuracy decreasing in P_<k+1> was investigated in a previous paper. This paper almost clarifies the phenomenon of accuracy decreasing in P_<k+i>, i= 1, 2, . . . , under the restriction that degrees of initial polynomials are not large. It is shown that if the close roots are concentrated at one point then the accuracy decreases at each calculation of P_<k+i>, i> O. If the close roots are distributed around r points, r> 1, which are mutually well-distant then the accuracy decreases each time the degree of remainder decreases by r. Furthermore, the amount of decrease of accuracy is clarified, with emphasis on the case P_2(x)z dP_1(x)/dx.
• 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 4, p. 394-403, 発行日 1990-03-15
• 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