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单词 Graeffe method
释义

Graeffe method

中文百科

当德兰-格拉夫方法 Graeffe's method

(重定向自Graeffe method)

Dandelin-Gräffe方法是求多项式根的数值方法之一,由几位18世纪数学家Karl Heinrich Gräffe、Germinal Pierre Dandelin和罗巴切夫斯基分别独立提出。

设欲解的方程为p(x) = (x-x_1)(x-x_2)...(x-x_n)

重复类似的步骤k次,可得以x_1^{2^k},x_2^{2^k}... \,\!为根的方程q,设y=x^{2^k} \,\!

q(y) = y^n + a_1y^{n-1} + ... + a_n

根据韦达定理:

若经过多次自乘后,这些根相差得足够大,使得:

对每个y_i2^k次根便可求得p(x)的根。

这个方法有缺点包括:

英语百科

Graeffe's method 当德兰-格拉夫方法

(重定向自Graeffe method)

In mathematics, Graeffe's method or DandelinGraeffe method is an algorithm for finding all of the roots of a polynomial. It was developed independently by Germinal Pierre Dandelin in 1826 and Karl Heinrich Gräffe in 1837. Lobachevsky in 1834 also discovered the principal idea of the method. The method separates the roots of a polynomial by squaring them repeatedly. This squaring of the roots is done implicitly, that is, only working on the coefficients of the polynomial. Finally, Viète's formulas are used in order to approximate the roots.

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更新时间:2025/6/27 5:40:10