Question

Hi, I need help with a fixed-point method program. It has to be done in C.

The inputs are: Initial approximation ρo, tolerance ε, and the maximum number of iterations MAXIT.

The outputs are: Approximate solution ρ or "solution not found".

STEP 1

Do i=1

STEP 2

While i≤ MAXIT, execute steps 3-6

STEP 3

Do ρ=ϕ(p) (calculate pi)

STEP 4

If |ρ-ρo|<ε then

output(ρ) (operation sucessful)

END

STEP 5

Do i=i+1

STEP 6

Do po=p (update po)

STEP 7

output (solution not found after MAXIT iterations)

END

Answer 1

main.c

#include<stdio.h>

#include<math.h>

float fixedPointIter(float);

int main()

{

float arr[100],arr1[100],arr2=100.0;

int x=1,y=0;

arr1[0]=(cos(0)-3*0+1);

printf("\nPlease enter initial guess:\n");

scanf("%f",&arr[0]);

printf("\n\n Values of iterations are:\n\n ");

while(arr2>0.00001)

{

arr[y+1]=fixedPointIter(arr[y]);

arr2=arr[y+1]-arr[y];

arr2=fabs(arr2);

printf("%d\t%f\n",y,arr[y]);

y++;

}

printf("\n Root of the function is %f",arr[y]);

  

  return 0;

}

float fixedPointIter(float x)

{

float y;

y=(cos(x)+2)/3;

return y;

}

Output:

Values of iterations are: 0 3.000000 1 0.336669 2 0.981287 3 0.851985 4 0.886164 5 0.877463 6 0.879701 7 0.879127 8 0.879275 9 0.879237 Root of the function is 0.8792