Linear Interpolation
For given points
x
0
x_0
x
0
and
x
1
x_1
x
1
, with
x
0
≠
x
1
x_0 \ne x_1
x
0
=
x
1
the linear interpolation is
p
1
(
x
)
=
f
(
x
0
)
+
(
f
(
x
1
)
−
f
(
x
0
)
x
1
−
x
0
)
(
x
−
x
0
)
p_1(x) = f(x_0) + (\frac{f(x_1)-f(x_0)}{x_1-x_0}) (x-x_0)
p
1
(
x
)
=
f
(
x
0
)
+
(
x
1
−
x
0
f
(
x
1
)
−
f
(
x
0
)
)
(
x
−
x
0
)
.
Interpolation Points
x
0
x_0
x
0
x
1
x_1
x
1
Function
f
(
x
)
=
1
2
x
+
2
f(x)=\frac{1}{2} x + 2
f
(
x
)
=
2
1
x
+
2
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
f
(
x
)
=
1
4
(
x
3
+
3
x
2
−
6
x
−
8
)
f(x)=\frac{1}{4} (x^3 + 3x^2 - 6x - 8)
f
(
x
)
=
4
1
(
x
3
+
3
x
2
−
6
x
−
8
)
f
(
x
)
=
2
x
4
−
3
x
3
+
5
x
2
−
x
+
7
f(x)=2x^4 - 3x^3 + 5x^2 - x + 7
f
(
x
)
=
2
x
4
−
3
x
3
+
5
x
2
−
x
+
7
References:
None