Added Bisection_Method.cpp (#2458)

Bisection_Method/Bisection_Method.cpp

@@ -0,0 +1,122 @@
+#include<iostream>
+#include<cmath>
+using namespace std;
+// approximation limit
+#define error 0.0001
+
+//function of the polynomial is inputted here say f(x) = x*x - 2*x + 1
+float polynomial(float x)
+{
+    return x * x - 4 * x + 3;
+}
+
+float mid(float q, float w)
+{
+    return (q + w) / 2;
+}
+
+int main()
+{
+    int i;
+    float lower_bound, upper_bound, a, b;
+
+    cout << "For the interval (a, b) where the root may lie : " << endl;
+    cout << "Enter the value of a :- " << endl;
+    cin >> lower_bound;
+
+    a = lower_bound;
+
+    cout << "Enter the value of b :- " << endl;
+    cin >> upper_bound;
+
+    b = upper_bound;
+
+    if(polynomial(lower_bound) * polynomial(upper_bound) > 0)
+    {
+        cout << "Invalid interval" << endl;
+    }
+    else
+    {   
+        // repeat until the required accuracy is obtained
+        while(abs(polynomial(mid(lower_bound, upper_bound))) > error)
+        {
+            cout << "\nIteration_no = " << i << " , First_no = " << lower_bound 
+            << " , Second_no = " << upper_bound << " middle = " 
+            << mid(lower_bound, upper_bound) ;
+            cout << " , f(middle) = " << polynomial(mid(lower_bound, upper_bound))
+            << " , f(first_no)*f(middle) = " 
+            << polynomial(lower_bound)*polynomial(mid(lower_bound, upper_bound)) << endl;
+            // sign changes in the first interval => root lies in the 1st interval
+            if(polynomial(lower_bound) * polynomial(mid(lower_bound, upper_bound)) < 0)
+            {
+                upper_bound = mid(lower_bound, upper_bound);
+            }
+            else
+            {
+                lower_bound = mid(lower_bound, upper_bound);
+            }
+            i++;
+        }
+        cout << "\nIteration_no = " << i << " , First_no = " << lower_bound 
+        << " , Second_no = " << upper_bound << " middle = " << mid(lower_bound, upper_bound) ;
+        cout << " , f(middle) = " << polynomial(mid(lower_bound, upper_bound)) 
+        << " , f(first_no)*f(middle) = " 
+        << polynomial(lower_bound)*polynomial(mid(lower_bound, upper_bound)) << endl;
+        cout << "\nThe approximated root of the given polynomial within the specified interval ("
+        << a << " , " << b << ") = " ;
+        cout << mid(upper_bound, lower_bound) << endl;
+    }
+    return 0;
+}
+
+/* OUTPUT
+For the interval (a, b) where the root may lie : 
+Enter the value of a :-
+2.1
+Enter the value of b :-
+4.1
+
+Iteration_no = 0 , First_no = 2.1 , Second_no = 4.1 middle = 3.1 , f(middle) = 0.21 ,
+f(first_no)*f(middle) = -0.2079
+
+Iteration_no = 1 , First_no = 2.1 , Second_no = 3.1 middle = 2.6 , f(middle) = -0.64 ,
+f(first_no)*f(middle) = 0.6336
+
+Iteration_no = 2 , First_no = 2.6 , Second_no = 3.1 middle = 2.85 , f(middle) = -0.2775 ,
+f(first_no)*f(middle) = 0.1776
+
+Iteration_no = 3 , First_no = 2.85 , Second_no = 3.1 middle = 2.975 , f(middle) = -0.0493755 ,
+f(first_no)*f(middle) = 0.0137017
+
+Iteration_no = 4 , First_no = 2.975 , Second_no = 3.1 middle = 3.0375 , f(middle) = 0.0764065 ,
+f(first_no)*f(middle) = -0.00377261
+
+Iteration_no = 5 , First_no = 2.975 , Second_no = 3.0375 middle = 3.00625 , f(middle) = 0.0125389 ,
+f(first_no)*f(middle) = -0.000619115
+
+Iteration_no = 6 , First_no = 2.975 , Second_no = 3.00625 middle = 2.99062 , f(middle) = -0.0186625 ,
+f(first_no)*f(middle) = 0.000921469
+
+Iteration_no = 7 , First_no = 2.99062 , Second_no = 3.00625 middle = 2.99844 , f(middle) = -0.00312233 ,
+f(first_no)*f(middle) = 5.82703e-005
+
+Iteration_no = 8 , First_no = 2.99844 , Second_no = 3.00625 middle = 3.00234 , f(middle) = 0.00469303 ,
+f(first_no)*f(middle) = -1.46532e-005
+
+Iteration_no = 9 , First_no = 2.99844 , Second_no = 3.00234 middle = 3.00039 , f(middle) = 0.000781059 ,
+f(first_no)*f(middle) = -2.43872e-006
+
+Iteration_no = 10 , First_no = 2.99844 , Second_no = 3.00039 middle = 2.99941 , f(middle) = -0.00117207 ,
+f(first_no)*f(middle) = 3.65958e-006
+
+Iteration_no = 11 , First_no = 2.99941 , Second_no = 3.00039 middle = 2.9999 , f(middle) = -0.000195503 ,
+f(first_no)*f(middle) = 2.29143e-007
+
+Iteration_no = 12 , First_no = 2.9999 , Second_no = 3.00039 middle = 3.00015 , f(middle) = 0.000292778 ,
+f(first_no)*f(middle) = -5.7239e-008
+
+Iteration_no = 13 , First_no = 2.9999 , Second_no = 3.00015 middle = 3.00002 , f(middle) = 4.86374e-005 ,
+f(first_no)*f(middle) = -9.50877e-009
+
+The approximated root of the given polynomial within the specified interval (2.1, 4.1) = 3.00002
+*/