数值分析课实验-求解线性方程组的直接法C代码

• 高斯顺序消元法
• 平方根法

---

//高斯顺序消元法

#include<stdlib.h>
#include<stdio.h>
#define N 10

 void gauss_shunxu(float a[N][N],float h[N]){
     int i,j,k;
     float x[N],temp1,temp2;
     for(k=0; k<N-1; k++){
            for(i=k + 1; i<N; i++){
                temp1=a[i][k]/a[k][k];
                h[i]-= h[k]*temp1;
                for(j=k+1; j<N; j++){
                        a[i][j]-=a[k][j]*temp1;
                }
            }
     }
     x[N-1]=h[N-1]/a[N-1][N-1];
     for(i=N-2; i>-1; i--){
            temp2=0;
            for(j=i+1; j<N; j++){
                temp2+=a[i][j]*x[j];
            }
            x[i]=(h[i]-temp2)/a[i][i];
     }
     printf("该线性方程组用Gauss顺序消元法求得的解为:\n");
     for(i=0; i<N; i++){
        printf("x%d=%lf\n",i+1,x[i]);
     }
 }

     void main() {
        float a[N][N]= {{4,2,-3,-1,2,1,0,0,0,0},
                          {8,6,-5,-3,6,5,0,1,0,0},
                          {4,2,-2,-1,3,2,-1,0,3,1},
                          {0,-2,1,5,-1,3,-1,1,9,4},
                          {-4,2,6,-1,6,7,-3,3,2,3},
                          {8,6,-8,5,7,17,2,6,-3,5},
                          {0,2,-1,3,-4,2,5,3,0,1},
                          {16,10,-11,-9,17,34,2,-1,2,2},
                          {4,6,2,-7,13,9,2,0,12,4},
                          {0,0,-1,8,-3,-24,-8,6,3,-1}};
        float h[N]= {5,12,3,2,3,46,13,38,19,-21};
        gauss_shunxu(a,h);
    }

运行截图：

//平方根法
#include
#include
#include
extern int flag=1;
int pingfanggenfa(double **a,double *b,int H)
{
    double *y = (double *) malloc(sizeof(double)*H);
    double s;
    int i,j,k;

    a[0][0] = sqrt(a[0][0]);              //求解a11
    for (i = 1; i < H; i++)               //第一列
        a[i][0] = a[i][0] / a[0][0];      //求解ai1
    for (k = 1; k < H; k++)               //第k列
    {
        for (i = k; i < H; i++)               //下三角，i>k
        {                                     //求aik
            for (s = 0, j = 0; j < k; j++)
                s += a[i][j] * a[k][j];     //求中间和
            if (i > k)                      //下三角元素
                a[i][k] = (a[i][k] - s) / a[k][k];
            else if (i == k)                //akk，主对角线元素
                a[i][k] = sqrt(a[i][k] - s);
        }
    }

    for(j = 0 ; j < H ; j++)
        for(i = j+1 ; i < H ; i++)
            a[j][i] = a[i][j];              //转置
    for(i = 0 ,flag = 0 ; i < H ; j++)
    {
        if(a[i][i] == 0)
        {
            printf("方程系数输入有误\n");
            flag = 1 ;                      //flag置1
        }break;
    }
    if(flag != 1){          // flag标志位不为0时继续计算
        y[0]= b[0] / a[0][0];           //先求y1
        for (k = 0; k < H; k++)
            {
           for (s = 0, j = 0; j < k; j++)
              s += a[k][j] * y[j];
           y[k] = (b[k] - s) / a[k][k];         //再求yk...n
        }
        b[H-1]= y[H-1] / a[H-1][H-1];   //先求xn
        for (k = H-2; k >= 0; k--)
        {
            for (s = 0, j = k+1; j < H; j++)
                s += a[j][k] * b[j];
                b[k] = (y[k] - s) / a[k][k];        //再求xi...1
        }
        printf("\nL的下三角矩阵为：\n");
            for(i = 0 ; i < H ; i++)
            {
                for(k = 0 ; k <= i ; k++)
                    printf("%lf   ",a[i][k]);
                printf("\n");
            }
            printf("\nL的转置矩阵为：\n");
            for(j = 0 ; j< H ; j++)
            {
                for(i = 0 ; i < H ; i++)
                {
                    if(i < j)
                        printf("           ");
                    else
                        printf("%lf   ",a[i][j]);
                }
                printf("\n");
            }
            printf("\nY的值为：\n");
            for(i = 0 ; i < H ; i++)
                printf("y%d=%lf\n",i+1,y[i]);
            printf("\nX的值为：\n");
            for(i = 0 ; i < H ; i++)
                printf("x%d=%lf\n",i+1,b[i]);
            free(y);                //释放动态开辟的空间
            return 0;
        }
    else if(flag == 1)
        flag = 1;       //flag标志位置1，退出
        return 0;
    }




    int main(){
    double **a  , *b;
    int i, j , H;
    while(flag == 1)
    {
        printf("请输入未知数个数n:\n");
        scanf("%d", &H);
        a = (double**)malloc(sizeof(double*)*H);    //为二维数组分配H行
        b = (double *) malloc(sizeof(double)*H);
        for (i = 0; i < H; i++)                                 //为每列分配H个大小空间
            a[i] = (double*)malloc(sizeof(double)*H);
            printf("请输入系数矩阵：\n");       //初始化
            for (i = 0; i < H; i++){
                for (j = 0; j < H; j++)
                    scanf("%lf",&a[i][j]);
            }
            printf("请输入向量b：\n");
            for (i = 0; i < H; i++){
                scanf("%lf",&b[i]);
            }
            pingfanggenfa(a,b,H);
    }
    free(b);                 //释放动态开辟的空间
    for (i = 0; i < H; ++i)
        free(a[i]);         //a行
        free(a);                //a列
}

运行截图：