セカント法を用いた逆関数補間テーブル

セカント法(Secant Method)
$x_{n+1}=x_n - f(x_n)\frac{x_n - x_{n-1}}{f(x_n)-f(x_{n-1})}$
で逆関数の値を事前に計算し, 後に線形補間で求めるメモ.

C#のプログラム. 初期値はx0=0.0, x1=1.0.

delegate double Func(double x);

static double estimate(Func f, double x0, double x1, double epsilon)
{
    int count = 0;
    double x2;
    while(epsilon < Math.Abs(f(x1))) {
        double d = f(x1)-f(x0);
        if(Math.Abs(d) < 1.0e-200) {
            break;
        }
        x2 = x1 - f(x1)*(x1-x0)/d;
        x0 = x1;
        x1 = x2;
        if(100 < ++count) {
            break;
        }
    }
    return x1;
}

static float[] createSampleTable(int resolution, Func f, double epsilon)
{
    float inv = 1.0f/resolution;
    float[] table = new float[resolution+1];
    for(int i = 0; i <= resolution; ++i) {
        float v = i*inv;
        double estimated = estimate((double x)=>f(x)-v, 0.0, 1.0, epsilon);
        table[i] = (float)estimated;
    }
    return table;
}