Civil Engineering Reference
In-Depth Information
f(x)
f(x
3
)
x
3
x
2
x
1
(x)
f(x
1
)
f(x
2
)
Figure 1.5.
Secant method.
The process of finding the new value is the same as linear interpolation
using Equation 1.1 to solve for a closer point between
x
1
= 1 and
x
2
= 1.25
.
()
−
()
()
−
()
=
(
)
−
(
)
xfxxfx
fx fx
102041 1251064
0 2041
.
.
−
.
1
2
2
1
x
=
=
1 2098
.
(
)
3
.
−−−
1 064
.
2
1
The reassignment of the values simply uses the last two values and their
corresponding functions as shown in Table 1.14.
Table 1.14.
Example 1.11 Secant method
1
2
3
4
x
1
1.25
1.2098
1.1994
1&2
2&3
f(x)
−1.0640
0.2041
0.0417
−
0.0025
This happens to be similar to the false position Example 1.10 as only inter-
polations occur, but with different sub-intervals.
1.10
nEWtOn-RAPHSOn MEtHOD OR
nEWtOn'S tAngEnt
The Newton-Raphson method uses more information about the function
to speed up convergence. It was originally developed by Issac Newton in
