C-code for Lab 1

Bisection Algorithm

/* Bisection Algorithm */

#include "stdio.h"
#include "math.h"

float Root(float left, float right, float tol, int *count);
int num;
float f(float x);
/* The root of the function f is found to within tol.
 The actual bisection algorithm is contained in a function
 called Root */
main()
{
float left, right, tol, root;
printf("Enter the left end point \n");
scanf("%f", &left);
printf("Enter the right end point \n");
scanf("%f", &right);
printf("Enter the tolerance \n");
scanf("%f", &tol);
if(f(left)*f(right) >=0)
	{printf("function values at end points have the same sign \n");
	 printf("Run the program again with another choice of end points \n");
	 return;}
num=0;
root=Root(left, right, tol, &num);
printf("The root is %f to within %f \n", root, tol);
printf("The number of iterations is %d \n", num);
}
float Root(float left, float right, float tol, int *count)
{
float p;
/* the root is bracketed by the values of left and right.
The value of p is the midpoint of this interval.
The variable count measures the number of times the algorithm
executes */
while(fabs(left-right) > tol) /* program stops when the interval < tol */
	{ 
	p=(left+right)/2.;
	if(f(p) ==0)  return p;
	if(f(p)*f(right) < 0) left=p; else right=p;
	(*count)++;
	}
return p;
}

float f(float x)
{
return (50/x)*(pow(1+.01*x,360)-1)-600;
}
/*units are in thousands of dollars
and x is the monthly interest rate measured in percent */



 Newton's Algorithm 


/* Bisection Algorithm */

#include 
#include 


int num;
float f(float x);
float df(float x);

/* The root of the function f is found to within tol
via Newton's method. The function is contained in f
and the derivative is contained in df
 */
main()
{
/* xnew contains the latest iterations of Newton
and xold contains the next to the latest iteration of Newton */

float xold, xnew, temp, tol;
int num;
printf("Enter an initial starting point \n");
scanf("%f", &xold);
printf("Enter the tolerance \n");
scanf("%f", &tol);
xnew=xold;
num=0; /* num is a counter index to check how many times the algorithm executes */
do
{
	xold=xnew; /* this step updates the algorithm for the next iteration */ 
	if(df(xold) == 0)  /* check to make sure there is no divide by zero */
		{printf("choose a new starting value and re-run the program \n");
		 return;}
	xnew=xold-(f(xold))/(df(xold));
	num++;
	if(num > 20) {printf("too many iterations \n"); return;}
	}
while(fabs(xold-xnew) > tol);  /* program stops when the interval < tol */


printf("The root is %f to within %f \n", xnew, tol);
printf("The number of iterations is %d \n", num);
}

float f(float x)
{
return (50/x)*(pow(1+.01*x,360)-1)-600;
}

float df(float x)
{
return -(50/(x*x))*(pow(1+.01*x,360)-1)+(180/x)*(pow(1+.01*x,359));
}
 

The Answers

/* The monthly interest rate is 0.576354 % */
/* The root of the polynomial x^3+x-1=0 is 0.6823278 */

Last updated 9/21/95