Initial data commit

Task/Steffensens-method/Go/steffensens-method.go

@@ -0,0 +1,75 @@
+package main
+
+import (
+    "fmt"
+    "math"
+)
+
+type fun = func(float64) float64
+
+func aitken(f fun, p0 float64) float64 {
+    p1 := f(p0)
+    p2 := f(p1)
+    p1m0 := p1 - p0
+    return p0 - p1m0*p1m0/(p2-2.0*p1+p0)
+}
+
+func steffensenAitken(f fun, pinit, tol float64, maxiter int) float64 {
+    p0 := pinit
+    p := aitken(f, p0)
+    iter := 1
+    for math.Abs(p-p0) > tol && iter < maxiter {
+        p0 = p
+        p = aitken(f, p0)
+        iter++
+    }
+    if math.Abs(p-p0) > tol {
+        return math.NaN()
+    }
+    return p
+}
+
+func deCasteljau(c0, c1, c2, t float64) float64 {
+    s := 1.0 - t
+    c01 := s*c0 + t*c1
+    c12 := s*c1 + t*c2
+    return s*c01 + t*c12
+}
+
+func xConvexLeftParabola(t float64) float64 {
+    return deCasteljau(2.0, -8.0, 2.0, t)
+}
+
+func yConvexRightParabola(t float64) float64 {
+    return deCasteljau(1.0, 2.0, 3.0, t)
+}
+
+func implicitEquation(x, y float64) float64 {
+    return 5.0*x*x + y - 5.0
+}
+
+func f(t float64) float64 {
+    x := xConvexLeftParabola(t)
+    y := yConvexRightParabola(t)
+    return implicitEquation(x, y) + t
+}
+
+func main() {
+    t0 := 0.0
+    for i := 0; i < 11; i++ {
+        fmt.Printf("t0 = %0.1f : ", t0)
+        t := steffensenAitken(f, t0, 0.00000001, 1000)
+        if math.IsNaN(t) {
+            fmt.Println("no answer")
+        } else {
+            x := xConvexLeftParabola(t)
+            y := yConvexRightParabola(t)
+            if math.Abs(implicitEquation(x, y)) <= 0.000001 {
+                fmt.Printf("intersection at (%f, %f)\n", x, y)
+            } else {
+                fmt.Println("spurious solution")
+            }
+        }
+        t0 += 0.1
+    }
+}