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

  var xold = a;
  var x0 = b;

  var fold = evaluateOn(xold);
  var fnew = evaluateOn(x0);
  var diff = tolerance + 1;

  while ((diff >= tolerance) && (n <= maxSteps)) {
    final den = fnew - fold;

    if ((den == 0) || (den.isNaN)) {
      throw NonlinearException(
        'Invalid denominator encountered. '
        'The invalid value for the denominator was $den',
      );
    }

    diff = -(fnew * (x0 - xold)) / den;
    xold = x0;
    fold = fnew;
    x0 += diff;

    diff = diff.abs();
    ++n;

    guesses.add(x0);
    fnew = evaluateOn(x0);
  }

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