二分法（计算方法）

1
//
采用二分法求方程 f(x)=x3-x-1=0在区间[1,2]内的一个实根, 使误差不超过0.001。要求给定方程条件和误差范围。

2

#include
"
iostream
"

3
#include
"
math.h
"

4

using

namespace
std;

5

float
fun(
float
x )

6
{

7

float
y;

8
y
=
x
*
x
*
x
-
x
-
1
;

9

return
y;

10
}

11
int
main()

12
{

13

14

float
a
=
1.0000
,b
=
2.0000
,x,y2,y1,m,n;
int
k;

15
printf(
"
k a b x f(x)\n
"
);

16
printf(
"
-----------------------------------------------------------\n
"
);

17

18

if
( fun(a)
*
fun(b)
>
0
)
return

0
;

19

else

20
{

21

22

for
( k
=
1
; fun(a)
*
fun(b)
<=
0
,k
<
12
;k
++
)

23
{

24

25
m
=
(b
-
a)
/
pow(
2
,k
+
1
);

26
x
=
(a
+
b)
/
2
;

27
y2
=
fun(x);

28
y1
=
fun(a);

29

30

if
(fabs(y2)
<
m)
return

0
;

31

if
(y1
*
y2
<
0
) { b
=
x; }

32

else
{ a
=
x ; y1
=
fun(x) ;}

33
n
=
(b
-
a)
/
pow(
2
,k
+
1
);

34

if
((b
-
a)
>=
n)

35

if
(k
<
10
) printf(
"
%d %.9lf %.9lf %.9lf %.9lf\n
"
,k,a,b,x,fun(x));

36

else
printf(
"
%d %.9lf %.9lf %.9lf %.9lf\n
"
,k,a,b,x,fun(x));

37

38
}

39

40
}

41

42

43
}

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