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+//Example 2.3

+clc

+clear

+

+function [root] = FalsePosition(fun,x,tol,maxit)

+// FalsePosition: Computes roots of the function in the given range using False Position Method

+//// Input: FalsePosition(fun,x,tol,maxit)

+// fun = function handle

+// x = range in between sign change is evident

+// tol = Maximum error between iterations that can be tolerated

+// maxit = Maximum number of iterations

+//// Output: [root]

+// Root: Root of the given function in defined range

+

+if fun(x(1)) > 0 then

+    xu = x(1);    xl = x(2);

+else

+    xu = x(2);    xl = x(1);

+end

+

+Ea = 1;

+iter = 1;

+

+while(1)

+    xr(iter) = xl(iter) - ((xu(iter)-xl(iter)) / (fun(xu(iter))-fun(xl(iter))) * fun(xl(iter)));

+    if fun(xr(iter)) > 0 then

+        xu(iter+1) = xr(iter);

+        xl(iter+1) = xl(iter);

+    elseif fun(xr(iter)) < 0 then

+        xl(iter+1) = xr(iter);

+        xu(iter+1) = xu(iter);

+    else

+        break

+    end

+    

+    if iter>1 then

+        Ea(iter) = 100 * abs((xr(iter) - xr(iter-1)) / xr(iter));

+    end

+   

+    if Ea(iter) < tol | iter == maxit then

+        break

+    end

+    iter = iter + 1;

+end

+root = xr(iter);

+endfunction

+

+function f = fun3(x)

+    f = log(x) - cos(x);

+endfunction

+

+x = [1 2];

+tol = 1e-4;

+maxit = 5;

+root = FalsePosition(fun3,x,tol,maxit);

+disp(round(root*10^4)/10^4,"root = ")