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Solve the equation \(f(x)=0\) using Newton-Raphson method for both real and complex solutions. More...
#include <cmath>#include <cstdint>#include <ctime>#include <iostream>#include <limits>
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static double eq (double i) static double eq_der (double i) int main () constexpr double EPSILON = 1e-10 system accuracy limitSolve the equation \(f(x)=0\) using Newton-Raphson method for both real and complex solutions.
The \((i+1)^\text{th}\) approximation is given by:
\[x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)} \]
Definition in file newton_raphson_method.cpp.
◆ eq()define \(f(x)\) to find root for. Currently defined as:
\[f(x) = x^3 - 4x - 9 \]
Definition at line 30 of file newton_raphson_method.cpp.
30 {
31 return (std::pow(i, 3) - (4 * i) - 9);
32}
◆ eq_der() double eq_der ( double i ) staticdefine the derivative function \(f'(x)\) For the current problem, it is:
\[f'(x) = 3x^2 - 4 \]
Definition at line 40 of file newton_raphson_method.cpp.
40 {
41 return ((3 * std::pow(i, 2)) - 4);
42}
◆ main()Main function
Definition at line 45 of file newton_raphson_method.cpp.
45 {
46 std::srand(std::time(nullptr));
47
48 double z = NAN, c = std::rand() % 100, m = NAN, n = NAN;
49 int i = 0;
50
51 std::cout << "\nInitial approximation: " << c;
52
53
57
58 z = c - (m / n);
59 c = z;
60
61 if (std::abs(m) < EPSILON) {
62 break;
63 }
64 }
65
66 std::cout << "\n\nRoot: " << z << "\t\tSteps: " << i << std::endl;
67 return 0;
68}
#define MAX_ITERATIONS
Maximum number of iterations to check.
static double eq(double i)
static double eq_der(double i)
◆ EPSILON ◆ MAX_ITERATIONS int16_t MAX_ITERATIONS = INT16_MAX constexprRetroSearch is an open source project built by @garambo | Open a GitHub Issue
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