solve method

@override ({double convergence, double efficiency, List<double> guesses}) solve()

Generates the succession generated by the root-finding algorithm. Returns a Record object whose members are:

• a guesses named field, which contains the list of values generated by the algorithm on each step;

• a convergence named field, whose value represents the convergence rate for the generated succession (computed using convergence).

• a efficiency named field, whose value represents the efficiency of the algorithm (computed using efficiency).

Implementation

@override
({List<double> guesses, double convergence, double efficiency}) solve() {
  // Exit immediately if the root is not bracketed
  if (evaluateOn(a) * evaluateOn(b) >= 0) {
    throw NonlinearException('The root is not bracketed in [$a, $b]');
  }

  final guesses = <double>[];
  var n = 1;

  var x0 = a;
  var x1 = b;
  var y0 = evaluateOn(x0);
  var y1 = evaluateOn(x1);

  while (n <= maxSteps) {
    final x2 = (x0 + x1) / 2;
    final y2 = evaluateOn(x2);

    // The guess on the n-th iteration
    final x = x2 + (x2 - x0) * (y0 - y1).sign * y2 / sqrt(y2 * y2 - y0 * y1);

    // Add the root to the list
    guesses.add(x);

    // Tolerance
    if (min<double>((x - x0).abs(), (x - x1).abs()) < tolerance) {
      break;
    }

    final y = evaluateOn(x);

    // Fixing signs
    if (y2.sign != y.sign) {
      x0 = x2;
      y0 = y2;
      x1 = x;
      y1 = y;
    } else {
      if (y1.sign != y.sign) {
        x0 = x;
        y0 = y;
      } else {
        x1 = x;
        y1 = y;
      }
    }

    ++n;
  }

  return (
    guesses: guesses,
    convergence: convergence(guesses, maxSteps),
    efficiency: efficiency(guesses, maxSteps),
  );
}