Graphics Programs Reference
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dx = (b - a)/2.0;
x=a+dx;
end
% Check for convergence
if abs(dx) < tol*max(b,1.0)
root = x; return
end
end
root = NaN
EXAMPLE 4.6
Aroot of
f
(
x
)
x
3
10
x
2
=
−
+
5
=
0lies close to
x
=
0
.
7
.
Compute this root with the
Newton-Raphsonmethod.
Solution
The derivative of the functionis
f
(
x
)
3
x
2
=
−
20
x
,
so that the Newton-
Raphson formulainEq. (4.3) is
x
3
10
x
2
2
x
3
10
x
2
f
(
x
)
f
(
x
)
=
−
+
5
−
−
5
←
−
−
=
x
x
x
20
)
It takes only two iterationstoreach five decimal place accuracy:
3
x
2
−
20
x
x
(
3
x
−
7)
3
7)
2
2(0
.
−
10(0
.
−
5
x
←
=
0
.
735 36
0
.
7
[
3(0
.
7)
−
20
]
735 36)
3
735 36)
2
2(0
.
−
10(0
.
−
5
x
←
=
0
.
734 60
0
.
735 36
[
3(0
.
735 36)
−
20
]
EXAMPLE 4.7
Find the smallest positivezeroof
x
4
4
x
3
45
x
2
f
(
x
)
=
−
6
.
+
6
.
+
20
.
538
x
−
31
.
752
Solution
60
40
20
0
-20
-40
0
1
2
3
4
5
x
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