newtonRaphson<T extends num> function

double newtonRaphson<T extends num>(double f(double x), double df(double x)?, T initialGuess, { int maxIter = 100, double tol = 1e-12, double epsDerivative = 1e-12, })

High-performance Newton–Raphson root finder with optional numeric derivative.

This implementation is written for production use: it performs a guarded iteration with optional analytic derivative fallback, configurable tolerances, and a robust step limit. It accepts generic numeric types but converts to double internally for numeric performance and interoperability.

Example usage:

final root = newtonRaphson((x) => x * x - 2, null, 1.0);

Implementation

double newtonRaphson<T extends num>(
  double Function(double x) f,
  double Function(double x)? df,
  T initialGuess, {
  int maxIter = 100,
  double tol = 1e-12,
  double epsDerivative = 1e-12,
}) {
  var x = initialGuess.toDouble();
  for (var i = 0; i < maxIter; i++) {
    final fx = f(x);
    final derivative =
        df != null ? df(x) : _numericDerivative(f, x, eps: epsDerivative);
    if (derivative == 0.0 || derivative.isNaN) {
      x += tol; // perturb and try again
      continue;
    }
    final dx = fx / derivative;
    x -= dx;
    if (dx.abs() <= tol * (1.0 + x.abs())) {
      return x;
    }
  }
  throw StateError('Newton–Raphson did not converge in $maxIter iterations');
}