[1]拉格朗日插值

程序设计流程[OCTAVE]：
[1]
n = 5
x = [-5:2:5]
y = 1./((x.*x)+1)
xi= [0.75:1:4.75]
interp1(x,y,xi)
n = 10
x = [-5:1:5]
y = 1./((x.*x)+1)
xi= [0.75:1:4.75]
interp1(x,y,xi)
n = 20
x = [-5:0.5:5]
y = 1./((x.*x)+1)
xi= [0.75:1:4.75]
interp1(x,y,xi)
[2]
n = 5
h = 2.0/n
x = [-1:h:1]
y = exp(x)
xi= [0.95,-0.05,0.05,0.95]
interp1(x,y,xi)
n = 10
h = 2.0/n
x = [-1:h:1]
y = exp(x)
xi= [0.95,-0.05,0.05,0.95]
interp1(x,y,xi)
n = 20
h = 2.0/n
x = [-1:h:1]
y = exp(x)
xi= [0.95,-0.05,0.05,0.95]
interp1(x,y,xi)
结果[OCTAVE]:
[1]
x 0.75 1.75 2.75 3.75 4.75
n = 5 Pn(x) 0.5000 0.3500 0.1500 0.0769 0.0462
n = 10 Pn(x) 0.6250 0.2750 0.1250 0.0691 0.0436
n = 20 Pn(x) 0.6500 0.2538 0.1190 0.0671 0.0428
f(x) 0.6400 0.2462 0.1168 0.0664 0.0424
[2]
xi 0.95 -0.05 0.05 0.95
n = 5 Pn(x) 2.6063 0.9697 1.0704 2.6063
n = 10 Pn(x) 2.5951 0.9547 1.0554 2.5951
n = 20 Pn(x) 2.5889 0.9524 1.0526 2.5889
f(x) 2.5857 0.9512 1.0513 2.5857