The principal nth root of a positive real number

java

Newton’s method

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public static double nthroot(int n, double A) {
  double r = nthroot(n, A, .001);
  return BigDecimal.valueOf(r).setScale(3, RoundingMode.HALF_DOWN).doubleValue();
}

public static double nthroot(int n, double A, double p) {
  if(A < 0) {
    System.err.println("A < 0");// we handle only real positive numbers
    return -1;
  } else if(A == 0) {
    return 0;
  }
  double x_prev = A;
  double x = A / n;  // starting "guessed" value...
  while(Math.abs(x - x_prev) > p) {
    x_prev = x;
    x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
  }
  return x;
}

Binary search strategy

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public static double root(double x, int n) {
  double lower = 0;
  double upper = x;
  double r = 0;
  double temp = 0;
  while (upper - lower >= 0.001) {
    r = (upper + lower) / 2;
    temp = Math.pow(r, n);
    if (temp > x) {
      upper = r;
    } else {
      lower = r;
    }
  }

  return BigDecimal.valueOf(r).setScale(3, RoundingMode.HALF_DOWN).doubleValue();
}

ref