实现高斯Seidel方法的C ++程序
高斯·赛德尔方法用于迭代求解线性方程组。这是一个用于实现高斯Seidel方法的C++程序。
算法
Begin
Take the dimensions of the matrix p and its elements as input.
Take the initials values of x and no of iteration q as input.
While q>0
Make a for loop i = 0 to p-1
initialize n[i] = (b[i] / a[i][i]).
Make a for loop i = 0 to p-1
If (j == i)
n[i] = n[i] - ((a[i][j] / a[i][i]) * m[j]).
m[i] = n[i].
Decrease q.
/*
Here, a[i][j] = input matrix.
b[i] = this array takes values of the right side of equation.
m[i] = stores initial values of x.
*/
Return 0
End示例
#include<iostream>
#include<conio.h>
using namespace std;
int main(void) {
float a[10][10], b[10], m[10], n[10];
int p = 0, q = 0, i = 0, j = 0;
cout << "Enter size of 2D array : ";
cin >> p;
for (i = 0; i < p; i++) {
for (j = 0; j < p; j++) {
cout << "a[" << i << ", " << j << " ]=";
cin >> a[i][j];
}
}
cout << "\nEnter values to the right side of equation\n";
for (i = 0; i < p; i++) {
cout << "b[" << i << ", " << j << " ]=";
cin >> b[i];
}
cout << "Enter initial values of x\n";
for (i = 0; i < p; i++) {
cout << "x:[" << i<<"]=";
cin >> m[i];
}
cout << "\nEnter the no. of iteration : ";
cin >> q;
while (q> 0) {
for (i = 0; i < p; i++) {
n[i] = (b[i] / a[i][i]);
for (j = 0; j < p; j++) {
if (j == i)
continue;
n[i] = n[i] - ((a[i][j] / a[i][i]) * m[j]);
m[i] = n[i];
}
cout<<"x"<<i + 1 << "="<<n[i]<<" ";
}
cout << "\n";
q--;
}
return 0;
}输出结果
Enter size of 2D array : 2 a[0, 0 ]=1 a[0, 1 ]=2 a[1, 0 ]=3 a[1, 1 ]=4 Enter values to the right side of equation b[0, 2 ]=1 b[1, 2 ]=2 Enter initial values of x x:[0]=0 x:[1]=0 Enter the no. of iteration : 3 x1 = 1. x2 = -0.25 x1 = 1.5 x2 = -0.625 x1 = 2.25 x2 = -1.1875