#/***********************************************************
#    delta2.rb -- Aitken (エイトケン) の $\Delta^2$ 法
#***********************************************************/

def delta2(n,  a)
    for j in 0...n
        i = j; while(i >=2)
            q = a[i] - 2 * a[i - 1] + a[i - 2]
            if (q == 0) 
                printf("収束しました.\n");  return
            end
            p = a[i] - a[i - 1]
            a[i - 2] = a[i] - p * p / q.to_f
            i -= 2
        end
        printf("%3d: % .14e\n", j, a[i])
    end
end

N = 50

a = []

# Euler's series $1 - 1!x + 2!x^2 - 3!x^3 + \cdots$ at $x = 0.1$ 
a[0] = t = 1
for i in 1...N
    t *= i * (-0.1);  a[i] = a[i - 1] + t
    printf("%2d % .14e\n", i, a[i])
end
delta2(N, a)

exit 0