Julia語言 例題1-7 已知3點的座標值 使用牛頓內插法求差除表？

Julia語言 例題1-7 已知3點的座標值 使用牛頓內插法求差除表？

x        f(x)
=============
0.0       0.0
1.0      -3.0
2.0       0.0
=============

程式
using Printf
x= [0.0 , 1.0  ,2.0]
f= [[ 0.0     ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
    [-3.0     ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
    [0.0      ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ]]

n=length(x)
println("  Divided Difference Table: ")
println("=============================")
for j=2:n
    for i=1:n-j+1
        f[i][j]=(f[i+1][j-1]-f[i][j-1])/(x[i+j-1]-x[i])
    end
end   

print("i\tx(i)\t\tf(i)\t\tf(i,i+1)\tf(i,i+1.i+2),  ......................\n")
for i=1:n
    s=@sprintf("%d\t%8.5f",i,x[i])
    print(s)
    for j=1:n-i+1
        s=@sprintf("\t%8.5f",f[i][j])
        print(s)
    end
    println()
 
end

輸出畫面
  Divided Difference Table: 
=============================
i x(i) f(i) f(i,i+1) f(i,i+1.i+2),  ......................
1 0.00000 0.00000 -3.00000 3.00000
2 1.00000 -3.00000 3.00000
3 2.00000 0.00000

Pn(x)= 0.0 + -3 (x-0.0) + 3 (x-0.0)(x-1.0) = 3x^2 -6x