Numerical Program

Secant Method Definition

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite difference approximation of Newton's method.

Equation: x2-4x-10

Features of Secant Method:

  • Type – open bracket
  • No. of initial guesses – 2
  • Convergence – super linear
  • Rate of convergence – faster
  • Accuracy – good
  • Programming effort – tedious
  • Approach – interpolation

Program of Secant Method in C Language

  #include<stdio.h>
  #include<conio.h>
  #include<math.h>
  #define ESP 0.0001
  #define F(x) x*x - 4*x - 10
  void main()
  {
  float x1,x2,x3,f1,f2,t;
  clrscr();
  printf("\nEnter the value of x1: ");
  scanf("%f",&x1);
  printf("\nEnter the value of x2: ");
  scanf("%f",&x2); 
  printf("\n________________________________________\n");
  printf("\n x1\t x2\t x3\t f(x1)\t f(x2)");
  printf("\n______________________________________________\n");
      do
      {
      f1=F(x1);
      f2=F(x2);
      x3=x2-((f2*(x2-x1))/(f2-f1));
      printf("\n%f %f %f %f %f",x1,x2,x3,f1,f2);
      x1=x2; 
      x2=x3;
      if(f2<0)
      {
      t=fabs(f2);
      }
      else
      {
      t=f2;
      }
      }
  while(t>ESP);
  printf("\n______________________________________________\n");
  printf("\n\nApp.root = %f",x3);
  getch();
  }
    

Output

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