Function aitken(f As Function(As Double) As Double, p0 As Double) As Double
    Dim As Double p1 = f(p0)
    Dim As Double p2 = f(p1)
    Dim As Double p1m0 = p1 - p0

    Return p0 - (p1m0 * p1m0) / (p2 - (2 * p1) + p0)
End Function

Function steffensenAitken(f As Function(As Double) As Double, pinit As Double, tol As Double, maxiter As Integer) As Double
    Dim As Double p0 = pinit
    Dim As Double p = aitken(f, p0)
    Dim As Integer iter = 1
    While Abs(p-p0) > tol Andalso iter < maxiter
        p0 = p
        p = aitken (f, p0)
        iter += 1
    Wend

    If Abs (p - p0) > tol Then Return 0 Else Return p
End Function

Function deCasteljau(c0 As Double, c1 As Double, c2 As Double, t As Double) As Double
    Dim As Double s = 1 - t
    Dim As Double c01 = (s * c0) + (t * c1)
    Dim As Double c12 = (s * c1) + (t * c2)
    Dim As Double c012 = (s * c01) + (t * c12)
    Return c012
End Function

Function xConvexLeftParabola(t As Double) As Double
    Return deCasteljau(2, -8, 2, t)
End Function

Function yConvexLeftParabola(t As Double) As Double
    Return deCasteljau(1, 2, 3, t)
End Function

Function implicitEquation(x As Double, y As Double) As Double
    Return (5 * x * x) + y - 5
End Function

Function f(t As Double) As Double
    Dim As Double x = xConvexLeftParabola(t)
    Dim As Double y = yConvexLeftParabola(t)

    Return implicitEquation(x, y) + t
End Function

Dim As Double t0 = 0

For i As Integer = 0 To 10
    Print Using "t0 = #.# : "; t0;
    Dim As Double t = steffensenAitken(@f, t0, 0.00000001, 1000)
    If t = 0 Then
        Print "no answer"
    Else
        Dim As Double x = xConvexLeftParabola(t)
        Dim As Double y = yConvexLeftParabola(t)

        If Abs(implicitEquation(x, y)) <= 0.000001 Then
            Print Using "intersection at (##.######, ##.######)"; x; y
        Else
            Print "spurious solution"
        End If
    End If
    t0 += 0.1
Next

Sleep