Create newtonRaphsonApplication.cpp

Applications/Computational_Algorithm_Applications/newtonRaphsonApplication.cpp

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+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+double function(double x) {
+    return x * x - 16.0; //f(x) = x^2 - 16
+}
+
+// The derivative of the function
+double derivative(double x) {
+    return 2.0 * x; // f'(x) = x^2 - 16 is 2x
+}
+
+// Newton-Raphson method
+double newtonRaphson(double initialGuess, double tolerance, int maxIterations) {
+    double x = initialGuess;
+
+    for (int i = 0; i < maxIterations; ++i) {
+        double f_x = function(x);
+        double f_prime_x = derivative(x);
+
+        if (abs(f_prime_x) < 1e-6) {
+            cout << "Derivative is too small. Cannot continue." << endl;
+            return x;
+        }
+
+        double x_next = x - (f_x / f_prime_x);
+
+        if (abs(x_next - x) < tolerance) {
+            cout << "Converged to a root after " << i + 1 << " iterations." << endl;
+            return x_next;
+        }
+
+        x = x_next;
+    }
+
+    cout << "Did not converge after " << maxIterations << " iterations." << endl;
+    return x;
+}
+
+int main() {
+    double initialGuess = 4.0;
+    double tolerance = 1e-6;
+    int maxIterations = 100;
+
+    double root = newtonRaphson(initialGuess, tolerance, maxIterations);
+    cout << "Approximate root: " << root << endl;
+
+    return 0;
+}