C Program for Secant Method

Algorithm initialize two guesses x1 and x2 set f1=f(x1) and f2=f(x2) compute, x3=((x1*f2)-(x2*f1))/(f2-f1) and set f3=f(x3) if ((x3-x...

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Algorithm

1. initialize two guesses x1 and x2
2. set f1=f(x1) and f2=f(x2)
3. compute, x3=((x1*f2)-(x2*f1))/(f2-f1) and set f3=f(x3)
4. if ((x3-x2)/x3)<=e, print root
5. else, set x1=x2, f1=f2, x2=x3, f2=f3 and goto step 3
6. exit

Program

#include<conio.h>

#include<stdio.h>

#include<math.h>

#define f(x) x*x*x-2*x-5

#define e 0.0001

void main()

{

float x1,x2,x3,f1,f2,f3,root;

int i=1;

clrscr();

printf("Secant Method to find root of x^3-2x-5=0\n");

printf("Enter initial guesses\n");

printf("x1: ");

scanf("%f",&x1);

printf("x2: ");

scanf("%f",&x2);

f1=f(x1);

f2=f(x2);

printf("steps\tx1\tf(x1)\tx2\tf(x2)\tx3\tf(x3)\n");

b:x3=((x1*f2)-(x2*f1))/(f2-f1);

f3=f(x3);

printf("%d\t%.4f\t%.4f\t%.4f\t%.4f\t%.4f\t%.4f\n",i,x1,f1,x2,f2,x3,f3);

i++;

if(fabs((x3-x2)/x3)<=e)

{

root=x3;

printf("The root is %.4f",root);

goto c;

}

else

{

x1=x2;

f1=f2;

x2=x3;

f2=f3;

goto b;

}

c:

getch();

}

Output