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フルテキストURL KJ00000156054.pdf ( 382.0KB ) 公開日 2010-04-19 代数方程式の数値解法 ダイスウ ホウテイシキ ノ スウチ カイホウ A Numerical Method for Polynomial Equations 岡田, 敏彦 オカダ, トシヒコ Okada, Toshihiko 山口大学工学部 In this paper author describes a method for finding roots of a polynomial. Let ƒ(z)=a_0z^n+a_1z^+…+a_n be a polynomial whose coefficients are complex. Using Lehmer's algorithm for ƒ(z), we can construct a polynomial sequence such that ƒ_0(z), ƒ_1(z), ……, ƒ_(z), ƒ_k. Besides, we calculate P_=|P_i|(|ƒ_(0)|^2-1)/(|ƒ_(0)|^2+1) where i=1,2,……, k and P_0=1. Let m be the maximum i such that |P_i|>d^<-t> where d (=2 or 10) is the base of the computer's number system and t is the number of digits in the mantissa of the float ng point system. Then we can obtain the number M of roots which ƒ(z) has in the unit circle by the recurrence formula so that M_=1(-P_i)n_+sgn(P_i) M_i where 1(x) is unit function, sgn(x) is sign function, i=m, m-1,……, 1 and M_m=0. Furthermore, we can know easily the number of roots of ƒ(z) in a circle of radius R by transforming ƒ(z) to ƒ(Rz). From this we can find as follows : (1) the circle Γ having one or more roots of ƒ(z) on itself, (2) the places of roots of ƒ(z) lying on Γ. The process for finding (1) and (2) is a second order. Also, this method can obtain double roots and roots of greater multiplicity. jpn 数学 text application/pdf 山口大学工学部 ヤマグチ ダイガク コウガクブ 紀要論文 0372-7661 AN00244228 山口大学工学部研究報告 山口大学工学部研究報告 Memoirs of the Faculty of Engineering, Yamaguchi University 25 1 1 5 1974 出版社版 本文データは国立情報学研究所において電子化したものである KJ00000156054 山口大学 http://www.lib.yamaguchi-u.ac.jp/yunoca/handle/KJ00000156054