1
COMPUTER SCIENCE 349A
Handout Number 25
CUBIC SPLINE INTERPOLATION
Example
:
the case
n
=
3.
o
o
o
o
S
(x)
0
S
(x)
S
(x)
1
2
h
0
h
1
h
2
x
0
x
1
x
2
x
3
o
denotes interpolated values
f(x
)
i
Condition (b) in the definition of a cubic spline interpolant implies that
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
3
3
2
2
2
2
1
1
1
0
0
0
x
f
x
S
x
f
x
S
x
f
x
S
x
f
x
S
=
=
=
=
Condition (c) implies that
)
(
)
(
above
from
or
)
(
)
(
)
(
)
(
above
from
or
)
(
)
(
2
1
2
2
1
2
2
1
0
1
1
0
1
1
x
S
x
f
x
S
x
S
x
S
x
f
x
S
x
S
=
=
=
=
Condition (d) implies that
′
S
1
(
x
1
)
=
′
S
0
(
x
1
)
′
S
2
(
x
2
)
=
′
S
1
(
x
2
)
Condition (e) implies that
′
′
S
1
(
x
1
)
=
′
′
S
0
(
x
1
)
′
′
S
2
(
x
2
)
=
′′
S
1
(
x
2
)

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