NumericalMethods.cs

/* Original code Copyright (c) 2018 Shane Celis[1]
   Licensed under the MIT License[2]

   Original code posted here[3].

   This comment generated by code-cite[4].

   [1]: https://github.com/shanecelis
   [2]: https://opensource.org/licenses/MIT
   [3]: https://gist.github.com/shanecelis/976f901fab5eebd3d68b479181999f01
   [4]: https://github.com/shanecelis/code-cite
*/

using System;

/*
  Burden, R. L., & Faires, J. D. (2005). Numerical analysis (8 ed.). Belmont, CA: Thomson Brooks/Cole.
 */
public static class NumericalMethods {

  /*
    This is known as the forward-difference formula if h > 0 and the
    backward-difference formula if h < 0 (Burden 168).
   */
  public static Func<float, float> Derivative(Func<float, float> f, float h) {
    return x => (f(x + h) - f(x)) / h;
  }

  /* Given a guess p_n, this will return p_{n + 1}. (Burden 64) */
  public static Func<float, float> NewtonsMethodStep(Func<float, float> f, Func<float, float> df) {
    // Returns p_{n + 1}
    return p_n => p_n - f(p_n) / df(p_n);
  }

  /* Find a root of an equation: Find the p where f(p) = 0. (Burden 65) */
  public static float NewtonsMethod(Func<float, float> f, Func<float, float> df, float p_0, float tolerance, int maxSteps) {
    var step = NewtonsMethodStep(f, df);
    int i = 0;
    float p = p_0;
    do {
      p_0 = p;
      p = step(p_0);
    } while (Math.Abs(p - p_0) > tolerance && i++ < maxSteps);
    return p;
  }

}