Find k 1 , k 2 , k 3 in the following cubic spline. Which of the three end conditions—natural, parabolically terminated, or not-a-knot—if any, are satisfied? S ( x ) = { 4 + k 1 x + 2 x 2 − 1 6 x 3 on [ 0 , 1 ] 1 − 4 3 ( x − 1 ) + k 2 ( x − 1 ) 2 − 1 6 ( x − 1 ) 3 1 + k 3 ( x − 2 ) + ( x − 1 ) 2 − 1 6 ( x − 2 ) 3 on [ 1 , 2 ] on [ 2 , 3 ]
Find k 1 , k 2 , k 3 in the following cubic spline. Which of the three end conditions—natural, parabolically terminated, or not-a-knot—if any, are satisfied? S ( x ) = { 4 + k 1 x + 2 x 2 − 1 6 x 3 on [ 0 , 1 ] 1 − 4 3 ( x − 1 ) + k 2 ( x − 1 ) 2 − 1 6 ( x − 1 ) 3 1 + k 3 ( x − 2 ) + ( x − 1 ) 2 − 1 6 ( x − 2 ) 3 on [ 1 , 2 ] on [ 2 , 3 ]
Find
k
1
,
k
2
,
k
3
in the following cubic spline. Which of the three end conditions—natural, parabolically terminated, or not-a-knot—if any, are satisfied?
S
(
x
)
=
{
4
+
k
1
x
+
2
x
2
−
1
6
x
3
on
[
0
,
1
]
1
−
4
3
(
x
−
1
)
+
k
2
(
x
−
1
)
2
−
1
6
(
x
−
1
)
3
1
+
k
3
(
x
−
2
)
+
(
x
−
1
)
2
−
1
6
(
x
−
2
)
3
on
[
1
,
2
]
on
[
2
,
3
]
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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