雅克比迭代算法

 

#include <iostream>
#include <string>
#include <vector>
#include <iomanip>
using namespace std;

const int n=3; //设置方程组的维


float a[n][n],x[n],b[n];

void input_data() //输入方程组的相关数据

{
    cout<<"输入方程组的系数矩阵a["<<n<<"]["<<n<<"]:"<<endl;
    for(int i=0;i<n;i++)
        for(int j=0;j<n;j++)
            cin>>a[i][j];
    cout<<"输入x[1,...,"<<n<<"]的初值:"<<endl;
    for(i=0;i<n;i++)
            cin>>x[i];
    cout<<"输入b[1,...,"<<n<<"]的初值:"<<endl;
    for(i=0;i<n;i++)
            cin>>b[i];
}

void output_equation() //输出方程组

{
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<n;j++)
        {
            if(j>0&&a[i][j]>0)
                cout<<"+";
            cout<<a[i][j]<<" x["<<j+1<<"] ";
        }
        cout<<"="<<b[i]<<endl;
    }
}

void main ()
{
    input_data();
    int counter; //设置计算时迭代的次数

    cout<<"输入迭代的次数"<<endl;
    cin>>counter;
    system("cls");
    output_equation();
    int k=0,i=0; //k用来统计迭代的次数;i用来表示x的序列

    float m_num1; //m_x用来保存x的原先值;m_num1用来计算j!=i的数据之和

    cout<<endl;
    cout<<"k\t";
    for(int j=0;j<n;j++)
        cout<<"x["<<j+1<<"]\t\t\t";
    cout<<endl;
    cout<<k<<"\t";
    k++;
    cout << setiosflags(ios::fixed); //和下一句结合起来用来设定小数位的位数

    cout << setprecision(10);
    float x_next[n];
    for(j=0;j<n;j++)
    {
        cout<<x[j]<<"\t\t";
    }
    cout<<endl;
    do
    {
        m_num1=0;
        for(j=0;j<n;j++)
        {
            if(j!=i)
                m_num1=m_num1+a[i][j]*x[j];
        }
        x_next[i]=(b[i]-m_num1)/a[i][i];
        if(i<n-1)
            i++;
        else
        {
            for(j=0;j<n;j++)
                x[j]=x_next[j];
            cout<<k<<"\t";
            for(j=0;j<n;j++)
                cout<<x[j]<<"\t\t";
            cout<<endl;
            i=0;
            k++;
        };
    }while(k<=counter);
}