例題1-9 已知六點的座標值 使用牛頓內插法 求差除表？

多項式內插法

例題1-9　已知六點的座標值 使用牛頓內插法　　求差除表？

n=6

x        f(x)
=============
0.0      -6.0
0.1      -5.89483
0.3      -5.65014
0.6      -5.17788
1.0      -4.28172
1.1      -3.99583
=============

'''
/* ex1-9-7.py is for developing the divided-defference
 * table for Newton Interpolation polynomial.
 */
n=6
x        f(x)
=============
0.0      -6.0
0.1      -5.89483
0.3      -5.65014
0.6      -5.17788
1.0      -4.28172
1.1      -3.99583
=============
'''
n=6
x= [0.0 for i in range(0,n)]     #x [n] 矩陣
f=  [ [0.0 for i in range(n)]  for j in range(n) ]       #[n] * [n] 矩陣
x= [0.0 , 0.1 , 0.3 ,0.6 , 1.0  , 1.1]
f= [[-6.0 ,  -5.89483   ,-5.65014  ,-5.17788 ,-4.28172  ,-3.99583 ],
      [0.0 ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
      [0.0 ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
      [0.0 ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
      [0.0 ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
      [0.0 ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ]]

print("\nNewton's Divided Interpolation : ")
print("\nEnter the value of n : ",n)
print("\nEnter the value of x[i] and f[i][0] : \n");
print("\tx[i]\t\tf[i][0]");
for i  in range (len(x)) : 
    print(  '\t',round(x[i],4),"\t\t",round( f[0][i],4))
print()

print("\n        Divided Difference Table:")
print(" =================================="  )

for i in range (1 ,n):
    for j in range (0 , n-i):
        f[i][j]=(f[i-1][j+1]-f[i-1][j]) / (x[i+j]-x[j])

print("i\tx(i)\tf(i)\t\t\tf(i,i+1)\tf(i,i+1.i+2),  ......\n");
for i in range (0 ,n):
    print ("{%d}\t{%2.5f}" %(i,x[i]), end='')
    for j in range (0 , n-i):
        print("\t{%2.5f}" %(f[j][i]) ,end='')
    print("\n")

======== RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/Ex1-9-7.py ===========

Newton's Divided Interpolation : 

Enter the value of n :  6

Enter the value of x[i] and f[i][0] : 

x[i] f[i][0]
0.0 -6.0
0.1 -5.8948
0.3 -5.6501
0.6 -5.1779
1.0 -4.2817
1.1 -3.9958


        Divided Difference Table:
 ==================================
i x(i) 　f(i) f(i,i+1) f(i,i+1.i+2),  ......

{0} {0.00000}{-6.00000}{1.05170}{0.57250}{0.21500}{0.06302} {0.01416}

{1} {0.10000}{-5.89483}{1.22345}{0.70150}{0.27802}{0.07859}

{2} {0.30000}{-5.65014}{1.57420}{0.95171}{0.35661}

{3} {0.60000}{-5.17788}{2.24040}{1.23700}

{4} {1.00000}{-4.28172}{2.85890}

{5} {1.10000}{-3.99583}

>>>

Ｐ(x)= {-6.00000} + {1.05170} (x-0.0) + {0.57250} (x-0.0) (x-0.1) + 
            {0.21500} (x-0.0) (x-0.1) (x-0.3) + {0.06302}(x-0.0) (x-0.1) (x-0.3) (x-0.6) +
           {0.01416} (x-0.0) (x-0.1) (x-0.3) (x-0.6) (x-1.0)