商g(x)/f(x)の高次導関数の公式について : 反復関数の次数と漸近誤差定数を定める一方法

概要

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In general, we can determine the order and the asymptotic error constant of a given iteration function by the comparison theorem. However, in the case when we feel difficult to expand the iteration function as the power series of u=f(x)/f'(x) or in the case of multiple roots, it is difficult to obtain them. In this paper, a formula of the higher derivative of the quotient g(x)/f(x) is given. By this formula, even in above cases, we can comparatively briefly determine the order and the asymptotic error constant of a given iteration function as compared with the comparison theorem.
一般社団法人情報処理学会の論文
1977-09-15