c++求解非线性方程组的牛顿顿迭代法(可编辑修改版).

cout<<"开始计算雅克比矩阵的逆矩阵 ："<<endl; for (i=0;i<N;i++)
{ for(j=0;j<N;j++) aug[i][j]=yy[i][j];
for(j=N;j<N2;j++) if(j==i+N) aug[i][j]=1; else aug[i][j]=0; }
for (i=0;i<N;i++) { for(j=0;j<N2;j++) cout<<aug[i][j]<<" "; cout<<endl; }
for (i=0;i<N;i++) x0[i]=x1[i];
} while (iter<Max);
return 0; }
void ff(float xx[N],float yy[N]) {float x,y; int i;
//调用函数
x=xx[0]; y=xx[1]; yy[0]=x*x-2*x-y+0.5; yy[1]=x*x+4*y*y-4;
cout<<"初始近似解向量："<<endl; for (i=0;i<N;i++)
cout<<x0[i]<<" "; cout<<endl;cout<<endl;
do {
iter=iter+1; cout<<"第 "<<iter<<" 次迭代开始"<<endl;
//计算向量函数的因变量向量 y0
ff(x0,y0);
计算近似解向量 x1
float x0[N]={2.0,0.25},y0[N],jacobian[N][N],invjacobian[N][N],x1[N],errornorm; int i,j,iter=0;
for( i=0;i<N;i++) cin>>x0[i];
//如果取消对 x0 的初始化，撤销下面两行的注释 符， 就可以由键盘向 x0 读入初始近似解向量
for (i=0;i<N;i++) { for(j=0;j<N2;j++) cout<<aug[i][j]<<" "; cout<<endl; for(j=N;j<N2;j++) inv[i][j-N]=aug[i][j]; }
cout<<endl;
The shortest way to do many things is
int i,j; float sum=0;
for(i=0;i<N;i++) { sum=0;
for(j=0;j<N;j++) sum=sum+inv[i][j]*y0[j]; x1[i]=x0[i]-sum;
}
cout<<"近似解向量："<<endl; for (i=0;i<N;i++) cout<<x1[i]<<" "; cout<<endl;cout<<endl;
cout<<"雅克比矩阵是： "<<endl; for( i=0;i<N;i++) {for(j=0;j<N;j++)
cout<<yy[i][j]<<" "; cout<<endl; } cout<<endl; }
void inv_jacobian(float yy[N][N],float inv[N][N]) {float aug[N][N2],L; int i,j,k;
cout<<"雅克比矩阵的逆矩阵： "<<endl; for (i=0;i<N;i++)
{ for(j=0;j<N;j++) cout<<inv[i][j]<<" ";
cout<<endl; } cout<<endl;
}
void newdundiedai(float x0[N], float inv[N][N],float y0[N],float x1[N]) {
// 差向量 1 范数的上限
#define Max 100
//最大迭代次数
using namespace std;
const int N2=2*N;
int main()
{
void ff(float xx[N],float yy[N]);
//计算向量函数的因变量向量 yy[N]
void ffjacobian(float xx[N],float yy[N][N]);/ /计算雅克比矩阵 yy[N][N]
cout<<endl;
for (i=0;i<N;i++) { for (k=i+1;k<N;k++) {L=-aug[k][i]/aug[i][i]; for(j=i;j<N2;j++) aug[k][j]=aug[k][j]+L*aug[i][j]; } }
The shortest way to do many things is
x=xx[0]; y=xx[1]; //jacobian have n*n element yy[0][0]=2*x-2;
//计算函数雅克比的值
The shortest way to do many things is
yy[0][1]=-1; yy[1][0]=2*x; yy[1][1]=8*y;
}
newdundiedai(x0, invjacobian,y0,x1); errornorm=0; for (i=0;i<N;i++) errornorm=errornorm+fabs(x1[i]-x0[i]); if (errornorm<Epsilon) break;
//计算差向量的 1 范数 errornorm
for (i=0;i<N;i++) { for(j=0;j<N2;j++) cout<<aug[i][j]<<" "; cout<<endl; }
cout<<endl;
for (i=N-1;i>0;i--) { for (k=i-1;k>=0;k--) {L=-aug[k][i]/aug[i][i]; for(j=N2-1;j>=0;j--) aug[k][j]=aug[k][j]+L*aug[i][j]; } }
The shortest way to do many things is
牛顿迭代法 c++程序设计
求解
0=x*x-2*x-y+0.5;
0=x*x+4*y*y-4;的方程
#include<iostream>
#include<cmath>
#define N 2
// 非线性方程组中方程个数、未知量个数
#define Epsilon 0.0001
void inv_jacobian(float yy[N][N],float inv[N][N]); //计算雅克比矩阵的逆矩阵 inv
void newdundiedai(float x0[N], float inv[N][N],float y0[N],float x1[N]); //由近似解向量 x0
//计算雅克比矩阵 jacobian
The shortest way to do many things is
ffjacobian(x0,jacobian);
//计算雅克比矩阵的逆矩阵 invjacobian
inv_jacobian(jacobian,invjacobian);
//由近似解向量Biblioteka Baidux0 计算近似解向量 x1
for (i=0;i<N;i++) { for(j=0;j<N2;j++) cout<<aug[i][j]<<" "; cout<<endl; }
cout<<endl;
for (i=N-1;i>=0;i--) for(j=N2-1;j>=0;j--) aug[i][j]=aug[i][j]/aug[i][i];
//计算初值位置的值
cout<<"向量函数的因变量向量是： "<<endl; for( i=0;i<N;i++)
cout<<yy[i]<<" "; cout<<endl; cout<<endl;
}
void ffjacobian(float xx[N],float yy[N][N]) {
float x,y; int i,j;