Neville interpolation

neville.cs

using System;

class Program
{
    static void Main()
    {
        var funcs = new Func<double, double>[8];
        funcs[0] = x => Math.Exp(x);
        funcs[1] = x => Math.Log(x);
        funcs[2] = x => 1 + x + x * x;
        for (var i = 3; i <= 7; i++)
        {
            var j = i;
            funcs[j] = x => funcs[j - 1](x) + Math.Pow(x, j);
        }

        var values = new double[8][,];
        for (var j = 0; j < 8; j++)
        {
            values[j] = new double[6, 2];
            for (var i = 5; i <= 10; i += 1)
                values[j][i - 5, 1] = funcs[j](values[j][i - 5, 0] = (i / 10d));
        }

        Console.WriteLine("Original value\t\tNeville interpolation\tDifference rate");
        for (var i = 0; i < 8; i++)
        {
            var nev = Neville(values[i]);
            var f = funcs[i](.75);
            var n = nev(.75);
            Console.WriteLine("{0}\t{1}\t{2}", f.ToString("e10"), n.ToString("e10"), Math.Abs((n - f) / f).ToString("e10"));
        }
    }

    static Func<double, double> Neville(double[,] values)
    {
        var len = values.GetLength(0);
        var funcs = new Func<double, double>[len, len];
        for (var i = 0; i < len; i++)
        {
            var j = i;
            funcs[j, j] = x => values[j, 1];
        }
        for (var i = 1; i < len; i++)
            for (var j = 0; j < len - i; j++)
            {
                var k = j;
                var l = j + i;
                funcs[k, l] = x => ((x - values[l, 0]) * funcs[k, l - 1](x) + (values[k, 0] - x) * funcs[k + 1, l](x)) / (values[k, 0] - values[l, 0]);
            }
        return funcs[0, len - 1];
    }
}