Check the spline conditions for { S 1 ( x ) = 1 + 2 x + 3 x 2 + 4 x 3 on [ 0 , 1 ] S 2 ( x ) = 10 + 20 ( x − 1 ) + 15 ( x − 1 ) 2 + 4 ( x − 1 ) 3 on [ 1 , 2 ] Regardless of your answer to (a), decide whether any of the following extra conditions are satisfied for this example: natural, parabolically terminated, not-a-knot.
Check the spline conditions for { S 1 ( x ) = 1 + 2 x + 3 x 2 + 4 x 3 on [ 0 , 1 ] S 2 ( x ) = 10 + 20 ( x − 1 ) + 15 ( x − 1 ) 2 + 4 ( x − 1 ) 3 on [ 1 , 2 ] Regardless of your answer to (a), decide whether any of the following extra conditions are satisfied for this example: natural, parabolically terminated, not-a-knot.
Solution Summary: The author explains that the given equation is a cubic spline. The property 1 of it is given by l
{
S
1
(
x
)
=
1
+
2
x
+
3
x
2
+
4
x
3
on
[
0
,
1
]
S
2
(
x
)
=
10
+
20
(
x
−
1
)
+
15
(
x
−
1
)
2
+
4
(
x
−
1
)
3
on
[
1
,
2
]
Regardless of your answer to (a), decide whether any of the following extra conditions are satisfied for this example: natural, parabolically terminated, not-a-knot.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.