帮我用c语言写一个改进平方根法求解方程组
时间: 2023-06-11 10:06:30 浏览: 135
好的,下面是用C语言实现改进平方根法求解方程组的代码:
```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define MAXN 100
void solve(double a[][MAXN], double b[], double x[], int n);
int main(void) {
int n;
double a[MAXN][MAXN], b[MAXN], x[MAXN];
printf("请输入方程组的个数 n: ");
scanf("%d", &n);
printf("请输入增广矩阵:\n");
for (int i = 0; i < n; i++) {
for (int j = 0; j <= n; j++) {
scanf("%lf", &a[i][j]);
}
}
solve(a, b, x, n);
printf("方程组的解为:\n");
for (int i = 0; i < n; i++) {
printf("x[%d] = %lf\n", i, x[i]);
}
return 0;
}
void solve(double a[][MAXN], double b[], double x[], int n) {
double p[MAXN], q[MAXN], y[MAXN], z[MAXN];
int i, j, k;
for (i = 0; i < n; i++) {
p[i] = a[i][i];
for (j = 0; j < i; j++) {
p[i] -= pow(q[j], 2);
}
q[i] = sqrt(p[i]);
for (j = i + 1; j < n; j++) {
q[j] = a[i][j];
for (k = 0; k < i; k++) {
q[j] -= q[k] * z[k * n + j];
}
q[j] /= q[i];
}
z[i * n + i] = 1;
for (j = i + 1; j < n; j++) {
z[i * n + j] = 0;
}
for (j = i; j < n; j++) {
for (k = i + 1; k < n; k++) {
z[k * n + j] = a[k][j] - q[k] * z[i * n + j];
}
}
}
y[0] = b[0] / q[0];
for (i = 1; i < n; i++) {
y[i] = b[i];
for (j = 0; j < i; j++) {
y[i] -= q[j] * y[j];
}
y[i] /= q[i];
}
x[n - 1] = y[n - 1] / z[(n - 1) * n + n - 1];
for (i = n - 2; i >= 0; i--) {
x[i] = y[i];
for (j = i + 1; j < n; j++) {
x[i] -= z[i * n + j] * x[j];
}
x[i] /= z[i * n + i];
}
}
```
这个程序使用了改进平方根法求解方程组,具体实现方法可以参考这个[链接](https://zh.wikipedia.org/wiki/%E6%94%B9%E8%BF%9B%E5%B9%B3%E6%96%B9%E6%A0%B9%E6%B3%95)。
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