雅可比迭代法和高斯赛德尔迭代法
刚学 Jacobi算法和Gauss_Siedel算法不久，觉的对以后学习会有帮助，所以记下来，希望感兴趣的朋友共勉！
雅克比迭代
#include
<
iostream
>
#include
"
math.h
"
using
namespace
std;
#define
n 3
double
a[n][n]
=
{{
5
,
2
,
1
},{
-
1
,
4
,
2
},{
2
,
-
3
,
10
}}, x[n]
=
{
-
3
,
2
,
1
}, b[n]
=
{
-
12
,
20
,
3
}, c[n];
int
i
=
0
,j,k
=
0
,counter
=
15
;
int
main()
{
int
k
=
0
,i
=
0
;
double
num1,E;
float
y[n];
do
{
E
=
0
;
for
(j
=
0
;j
<
n;j
++
)
{
c[j]
=
x[j];
}
num1
=
0
;
for
(j
=
0
;j
<
n;j
++
)
{
if
(j
!=
i)
num1
=
num1
+
a[i][j]
*
x[j];
}
for
(j
=
0
;j
<
n;j
++
)
{
c[j]
=
x[j];
}
y[i]
=
(b[i]
-
num1)
/
a[i][i];
if
(i
<
n)
{ i
++
; }
else
{
for
(j
=
0
;j
<
n;j
++
)
{ x[j]
=
y[j]; }
for
(j
=
0
;j
<
n;j
++
)
{
if
(E
<
(
float
)fabs(c[j]
-
y[j])) E
=
(
float
)fabs(c[j]
-
y[j]);
}
if
(k
>=
7
)
{ cout
<<
"
Iterations is
"
<<
k
+
1
<<
"
,
"
<<
"
Iterative precision is
"
;
printf(
"
%.6lf\n
"
,E);
for
(j
=
0
;j
<
n;j
++
)
printf(
"
x[%d]=%.5lf\t
"
,j,x[j]);
cout
<<
endl
<<
endl;
}
i
=
0
;
k
++
;
if
(E
<
0.001
)
break
;
}
}
while
(k
<=
counter);
cout
<<
"
Iterations is
"
<<
k
<<
endl;
cout
<<
"
Iterative terminating condition
"
;
printf(
"
x[%d]-x[%d]oo<%.6lf\n
"
,k,k
-
1
,E);
cout
<<
"
\t\t---------Solution-----------
"
<<
endl;
for
(i
=
0
;i
<
n;i
++
)
{
printf(
"
x[%d]=%.5lf\n
"
,i,x[i]);
}
}
高斯-赛德尔迭代法
#include
<
iostream
>
#include
<
math.h
>
using
namespace
std;
int
main()
{
double
a[
3
][
3
]
=
{{
1
,
2
,
-
2
},{
3
,
1
,
-
1
},{
2
,
4
,
1
}},b[
3
]
=
{
10
,
12
,
-
20
};
double
x[
3
]
=
{
0
,
0
,
0
},sum1,sum2;
int
i,j,k,n
=
3
;
for
(k
=
0
;k
<
5
;k
++
)
{
for
(i
=
0
;i
<
n;i
++
)
{ sum1
=
0
;sum2
=
0
;
for
(j
=
0
;j
<
i
-
1
;j
++
)
{ sum1
=
sum1
+
a[i][j]
*
x[j];
}
for
(j
=
i
+
1
;j
<
n;j
++
)
{sum2
=
sum2
+
a[i][j]
*
x[j];}
x[i]
=
(b[i]
-
sum1
-
sum2)
/
a[i][i];
}
for
(i
=
0
;i
<
n;i
++
)
{ printf(
"
x%d=%-15f
"
,i
+
1
,x[i]);}
printf(
"
\n
"
);
}
}