第一题、插值公式：
[ ]
( )
( ) ( )( ) ( )
0 1
0
0 1 1
, , ,
k
j
k
j
j j j j j j k
f x
f x x x
x x x x x x x x
=
- +
=
- - - -
å
L
L L
(1.1)
( )( ) ( )
1 0 1
( )
n n
x x x x x x x
w
+
= - - -L
( ) ( )
1
0
1
( )
( )
n
n
n k
k
k n k
x
L x y
x x x
w
w
+
¢
=
+
=
-
å
( )
[ ]
( )
[ ]
( )( )
[ ]
( ) ( )
[ ]
0 0 1 0 0 1 2 0 1 0 1 0 1 0 1
( ) , , , , , , , , , ( ) ( ) ( )
n n n n n n
f x f x f x x x x f x x x x x x x f x x x x x x x f x x x x P x R x
w
- +
= + - + - - + + - - + = +L L L L
0 0 0
1 1 1 1
1 1 1 1
2
2
2
2
n n n n
n n n
M d
M d
M d
M d
l
m l
m l
m
- - - -
æ öæ ö æ ö
ç ÷ç ÷ ç ÷
ç ÷ç ÷ ç ÷
ç ÷ç ÷ ç ÷
=
ç ÷ç ÷ ç ÷
ç ÷ç ÷ ç ÷
ç ÷ç ÷ ç ÷
è øè ø è ø
O O O M M
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
0 0 , 0 0 , 0 0 0 0 , 0 0 , 0 0
j j j j j j j j j j j j
S x S x S x S x S x S x S x S x S x S x S x S x
¢ ¢ ¢¢ ¢¢ ¢ ¢ ¢¢ ¢¢
- = + - = + - = + - = + - = + - = +
( 1)
1
( )
( ) ( ) ( ) ( )
( 1)!
n
n n n
f
R x f x L x x
n
x
w
+
+
= - =
+
0 1 1
0 1 1
( ) ( )( ) ( )
( ) , 0,1, ,
( ) ( )( ) ( )
k k n
k
k k k k k k n
x x x x x x x x
l x k n
x x x x x x x x
- +
- +
- - - -
= =
- - - -
L L
L
L L
0
( ) ( ) , 0,1, ,
n
n j k k j i
k
L x y l x y j n
=
= = =
å
L
第二题、拟合公式：
