逆数補間についての内容です。

質問

こんにちは。
私は、大学生で、補間についての勉強をしているものです。今回、始めて、洋書を読むことになり苦戦しております。以下の内容はどういったものなのでしょうか？アドバイスをいただきたいと思い、書かせてもらいました。
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[Inverse Interpolation]
A process called inverse interpolation is often used to approximate an inverse function. Suppose that values {Yi}=f({Xi}) have been computed at X0,X1,...,Xn.
Using table
Y ; Y0 Y1 Y2 ......Yn
X ; X0 X1 X2 ......Xn
we form the interpolation polynomial

p(y)=Σ(i=1→n)CiΠ(j=0→i-1){Y－Yj}
The orijinal relationship, y=f(x), has an inverse, under certain conditions. This inverse is being approximated by x=p(y). Procedures Coef and Eval can be used to carry out the inverse interpolation by reversing the arguments x and y in the calling sequence for Coef.
Inverse interpolation can be used to find where a given functuin f has a root or zero. This means inverting the equation f(x)=0. We propose to do this by creating a table of values (f(Xi),Xi) and interpolating with a polynomial,p. Thus, p(Yi)=Xi. The points Xi should be chosen near the unknown root,r. The approximate root is then given by r ～p(0). For a concrete case, let the table of known values be

Y;-0.5789200,-0.3626370,-0.1849160,-0.0340642,0.0969858

X; 1.0 , 2.0 , 3.0 , 4.0 , 5.0
The nodes in this problem are the points in the row of the table headed y, and the function values being interpolated are in the x row. The resulting polynomial is

p(Y)=0.25Y^4＋1.2Y^3＋3.69Y^2＋7.39Y＋4.247470086

and p(0)=4.247470086. Only the last coefficient is shown with all the digits carried in the calculation, for it is the only one needed for the problem at hand.
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自分で計算しても、p(Y)=0.25Y^4＋1.2Y^3＋3.69Y^2＋7.39Y＋4.247470086　となりません（泣）

回答No.1

noname#101087 · ベストアンサー

>[Inverse Interpolation]

引用テキストは、逆関数の補間を "inverse interpolation" と呼んでますね。

たまたま EXCEL シートの "Lagrange 補間多項式" 例題シートがあったので、挙げられている具体例を試行してみました。
　X=p(Y)=0.2504105*Y^4+1.2156411*Y^3+3.6940309*Y^2+7.3892454*Y+4.2474700
"The resulting polynomial" とほぼ同じです。
(X; 1.0, 2.0, 3.0, 4.0, 5.0 を入れてみてください)

回答No.2

noname#101087

#1 です。末尾を訂正。
>(X; 1.0, 2.0, 3.0, 4.0, 5.0 を入れてみてください)

(Y;-0.5789200,-0.3626370,-0.1849160,-0.0340642,0.0969858 を入れてみてください。X; 1.0, 2.0, 3.0, 4.0, 5.0 になります)