Question

This program has to be written in matlab

2. Write a function to find a root of f(c) using the secant method. Call this routine secant, call the file secant.m; its first line should be function [x,nf] = secant (fname, x0, x1, tol) fname is the name of the m-file which evaluates the function f(x), 20 and 21 are initial approximations to .c", and tol is a stopping tolerance. Your code should return an approximation x = 2X+1 to 3* so that **+1 - 2<tol, or a report of failure. Also, return nf, the total number of function evaluations of fname) executed.

Answer 1

function [x1,nf]=secant(fname,x0,x1,tol)
x(1)=x0;
x(2)=x1;

max_iter=100;
%secont method
k=2;
nf=0;
err=0.1; %intial error
while (abs(err) > tol & k<=max_iter)
x(k+1)=x(k)-fname(x(k))*(x(k)-x(k-1))/(fname(x(k))-fname(x(k-1)));
  
err = abs(x(k+1)-x(k));
  
k = k+1;

nf=nf+1;
end

x1=x(end);

  
end

function [xl, nf]=secant (fname, x0, xl, tol) x(1)=x0; x(2)=xl; 6bcoonWN max_iter=100; $secont method k=2; nf=0; err=0.1; fintial error Çwhile (abs (err) > tol & k<=max_iter) x (k+1)=x (k) -Ename (x (k))*(x (k) -x (k-1))/([name (x (k))-Ename (x (k-1))); err = abs(x (k+1)-x(k)); k = k+1; nf=nf+1; end SOCO S xl=x (end); end