Lin's Method

/* The following C program implements Lin’s method for determining the complex root of a polynomial equation, by extracting a quadratic factor of the form x2 + Px + Q from a polynomial equation. The polynomial and the initial approximations to P and Q are read as input. */

Source code:

#include<stdio.h>

#include<math.h>

#define max 10

#define min 0.0005

void main()

{

 float a[max], b[max], p, q, error, tempp, tempq;

 int i, degree, j=0;

 /* accepting the polynomial equation in the following form,

            xⁿ + a₀x^n-1 + a₁x^n-2 +……….+ a_n-2x + a_n-1 = 0      */

 printf("\n Enter degree of polynomial?  ");

 scanf("%d",&degree);

 for(i=degree; i>=0; i--)

 {

  printf("\n Enter coefficient of x^%d:  ",i);

  if(i<degree)

  {

             scanf("%f",&a[degree-1-i]);

             a[degree-1-i]/=a[degree];

  }

  else

            scanf("%f",&a[i]);

  }

  a[degree]=1;

  printf("\n X^2 + PX + Q \n Enter guesses for P and Q:  ");

  scanf("%f %f",&p,&q);

  error=1;

  while(error>=min)

  {

            for(i=0;i<=degree-3;i++)

           

if(i==0)

               b[i]=a[i]-p;

             else if(i==1)

                        b[i]=a[i]-p*b[i-1]-q;

             else

                   b[i]=a[i]-p*b[i-1]-q*b[i-2];

             tempq=q;

             q=a[degree-1]/b[degree-3];

             tempp=p;

             p=(a[degree-2]-q*b[degree-4])/b[degree-3];

             tempp=fabs(p-tempp);

             tempq=fabs(q-tempq);

             if(tempp>tempq)

                         error=tempp;

             else

                         error=tempq;

            j++;                                                      /* iteration no. */

  }

  printf("\n\n X^2 + %.3f*X + %.3f",p,q);

  printf("\n\n ---> Total iterations = %d",j);

  }

Output: