Question

c语言 迭代法

用迭代法求X=sqrt(a).求平方根的迭代公式为:
x=(1/2)(x+a/x)
要求前后两次求出的X的差的绝对值小于10e-6

Answer 1

#include<stdio.h>
double fabs(double n)
{
if (n < 0)
return -n;
return n;
}
main()
{
int n;
double x0,x1;
while (scanf("%d",&n) == 1)
{
x0 = 1;
x1 = (x0 + n / x0) / 2;
while(fabs(x1 - x0) > 0.000001)
{
if (fabs(x1 - x0) > 0.000001)
{
x0 = x1;x1 = (x0 + n / x0) / 2;
}
else
break;
}
printf("%.3lf\n",x1);
}
}

Answer 2

#include <stdio.h>
#include <math.h>

double diedai(double x,double a);

double sqrt(double a);

double sqrt(double a)
{
double x;
x=a/2;
return(diedai(x,a));
}

double diedai(double x,double a)
{
double y;
y=(x+a/x)/2; /*迭代公式*/
if((fabs(x-y))>10e-6) /*在不符合条件时进入迭代*/
{
y=diedai(y,a);
}
return(y);
}
void main(void)
{
double a,x;
printf("Input a:\n"); /*输入要求平方根的数*/
scanf("%lf",&a);
x=sqrt(a);
printf("Result %lf:\n",x);/*显示结果*/
}