next up previous
Next: What is New Here? Up: nr2 Previous: nr2

Simple Functions:

The Newton Raphson method works with many functions, and not just the $4x - cos(x)$ of the previous chapter. So it is convenient to separate the Newton-Raphson machinery, which is unchanged, from the function, whose roots we seek and which may be changed from one application to the next. Separating code into modular functional units is a highly desirable software engineering practice. We do this by using a subprogram.

Here is the same code as in the previous lesson, but it uses subprograms for evaluating the function and its derivative.

// Primitive code for finding roots of a function
// using the Newton-Raphson method

// Physics 6720 8/18/03

// Usage

//   nr

// The user is prompted for the tolerance and the starting point.

#include <iostream>
#include <cmath>
#define N 100    // Maximum number of iterations
using namespace std;

double f(double x){
   return 4*x - cos(x);
double dfdx(double x){
   return 4 + sin(x);

int main(){
  double p,pnew;
  double tol;
  int i;

  cout << "Enter tolerance: ";
  cin >> tol;
  cout << "Enter starting value x: ";
  cin >> pnew;

  // Main loop
  for(i = 0; i < N; i = i + 1){
    p = pnew;
    // The Newton-Raphson step
    pnew = p - f(p)/dfdx(p);
    // Check for convergence and quit if done
    if(fabs(p-pnew) < tol){
      cout << "Root is " << pnew << " to within " 
	   << tol << "\n";
      return 0;
  // We reach this point only if the iteration failed to converge
  cerr << "Failed to converge after " << N << " iterations.\n";
  return 1;


Carleton DeTar 2007-08-17