计算方法第四讲函数插值.pdf
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1
2 Lagrange
3 Newton
4
5 Hermite
6
7
1
1
1
2
[a,b] f (x)n+ 1
n n
{ }
x ⊂[a, b] { }
i i 0 f (x )
i i 0
Φϕ(x) ϕ (x ) f (x ), i 0,1, L, n
i i
n
{ }
ϕ(x)f (x)Φ xi i 0
f (x)[a,b]
ϕ (x ) f (x ), i 0,1, L, n n
{ }
x
i i i i 0
ϕ(x)
ϕ(x)
Φn
{ 2 n }
P ϕ (x) ϕ (x) a + a x + a x + L+ a x , a ∈R , 0 ≤ i ≤ n
n 0 1 2 n i
3
ϕ (x) a + a x + a x 2 + L+ a x n
0 1 2 n
ϕ(x)ϕ (x ) f (x ), i 0,1, L, n
i i
ϕ(x)
⎧ 2 n
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