ニュートン法

Newton.cs

using System;

namespace AppliedITEnginnerMisc
{
    /// <summary>
    /// ニュートン法の実装
    /// </summary>
    public sealed class Newton
    {
        /// <summary>
        /// f(x)
        /// </summary>
        private readonly Func<double, double> _func;

        /// <summary>
        /// f'(x)
        /// </summary>
        private readonly Func<double, double> _differentiated;

        /// <summary>
        /// 収束判定値
        /// </summary>
        public double E { get; set; }

        /// <summary>
        /// constructor
        /// </summary>
        /// <param name="func">非線形方程式 f(x) = 0 の左辺</param>
        /// <param name="differentiated">f(x) の微分</param>
        public Newton(Func<double, double> func, Func<double, double> differentiated)
        {
            _func = func;
            _differentiated = differentiated;
        }

        /// <summary>
        /// ニュートン法により非線形方程式 func(x) = 0 の実根の近似値を求めます
        /// </summary>
        /// <param name="initial">初期値</param>
        /// <returns>近似値</returns>
        public double Calc(double initial)
        {
            // x1 = x0 - (f(x0) / f'(x0))
        
            double x0;
            double x1 = initial;

            do
            {
                x0 = x1;
                x1 = (x0 - (_func(x0) / _differentiated(x0)));
            } while ((Math.Abs(x0 - x1)) >= this.E);

            return x1;
        }
    }
}

NewtonTest.cs

using AppliedITEnginnerMisc;
using Xunit;
using Xunit.Abstractions;

namespace Tests
{
    public class NewtonTest
    {
        private readonly ITestOutputHelper _output;

        public NewtonTest(ITestOutputHelper output)
        {
            _output = output;
        }

        [Fact]
        public void Test1()
        {
            // x^2 - 16 = 0 のひとつの実根をもとめてみる
            // f(x) = x^2 - N
            // f'(x) = 2x
            var newton = new Newton(x => x * x - 16, x => 2 * x)
            {
                E = 1
            };
            
            _output.WriteLine(newton.Calc(3).ToString());

            newton.E = 0.0001;
            _output.WriteLine(newton.Calc(3).ToString());

            newton.E = 0.0000001;
            _output.WriteLine(newton.Calc(6).ToString());
        }
    }
}