chore: import upstream snapshot with attribution

numerical_methods/newton_raphson_method.cpp

@@ -0,0 +1,68 @@
+/**
+ * \file
+ * \brief Solve the equation \f$f(x)=0\f$ using [Newton-Raphson
+ * method](https://en.wikipedia.org/wiki/Newton%27s_method) for both real and
+ * complex solutions
+ *
+ * The \f$(i+1)^\text{th}\f$ approximation is given by:
+ * \f[
+ * x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)}
+ * \f]
+ *
+ * \author [Krishna Vedala](https://github.com/kvedala)
+ * \see bisection_method.cpp, false_position.cpp
+ */
+#include <cmath>
+#include <cstdint>
+#include <ctime>
+#include <iostream>
+#include <limits>
+
+constexpr double EPSILON = 1e-10;              ///< system accuracy limit
+constexpr int16_t MAX_ITERATIONS = INT16_MAX;  ///< Maximum number of iterations
+
+/** define \f$f(x)\f$ to find root for.
+ * Currently defined as:
+ * \f[
+ * f(x) = x^3 - 4x - 9
+ * \f]
+ */
+static double eq(double i) {
+    return (std::pow(i, 3) - (4 * i) - 9);  // original equation
+}
+
+/** define the derivative function \f$f'(x)\f$
+ * For the current problem, it is:
+ * \f[
+ * f'(x) = 3x^2 - 4
+ * \f]
+ */
+static double eq_der(double i) {
+    return ((3 * std::pow(i, 2)) - 4);  // derivative of equation
+}
+
+/** Main function */
+int main() {
+    std::srand(std::time(nullptr));  // initialize randomizer
+
+    double z = NAN, c = std::rand() % 100, m = NAN, n = NAN;
+    int i = 0;
+
+    std::cout << "\nInitial approximation: " << c;
+
+    // start iterations
+    for (i = 0; i < MAX_ITERATIONS; i++) {
+        m = eq(c);
+        n = eq_der(c);
+
+        z = c - (m / n);
+        c = z;
+
+        if (std::abs(m) < EPSILON) {  // stoping criteria
+            break;
+        }
+    }
+
+    std::cout << "\n\nRoot: " << z << "\t\tSteps: " << i << std::endl;
+    return 0;
+}