Newton's Method

newtonmethod.m

// A quick-and-dirty implementation of Newton's method. Could use some tlc. May loop infinitely for certain inputs.

typedef CGFloat (^CalculateEquationBlock)(CGFloat x);

CGFloat NIFindRoot(CalculateEquationBlock fn, CalculateEquationBlock fndx, CGFloat guess) {
  CGFloat root = guess;
  while (1) {
    CGFloat newRoot = root - fn(root) / fndx(root);
    if (fabsf(newRoot - root) < 0.001) { // or whatever epsilon you want
      return newRoot;
    }
    root = newRoot;
  }
  return root;
}