Civil Engineering Reference
In-Depth Information
f(x)
f(x
1
)
x
2
(x)
x
1
x
3
f(x
2
)
Figure 1.4.
Method of false position or linear interpolation.
If the first interval contains the root, the values for the next cycle for
x
1
and
x
2
and the corresponding functions
f
(
x
1
) and
f
(
x
2
)
are as follows:
x
1
and
f
(
x
1
) remain unchanged
x
2
=
x
3
f
(
x
2
)
= f
(
x
3
)
If the second interval contains the root, then the values are used for
x
1
and
x
2
and the corresponding functions
f
(
x
1
) and
f
(
x
2
) are as follows:
x
2
and
f
(
x
2
) remain unchanged
x
1
=
x
3
f
(
x
1
) =
f
(
x
3
)
The process is continued until the desired accuracy is obtained.
Example 1.10
Method of false position
Refine the search of the function from Example 1.7 between 1.0 and 1.25
using the false position method to increase the accuracy of the approxi-
mate root. For the accuracy test use
ε
=
0.01 that is |
f
(
x
)| <
ε
:
x
3
−
84
.
x
2
+
20 16
.
x
−
13 824
.
=
0
