Data commit

Task/Steffensens-method/FreeBASIC/steffensens-method.basic

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+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