Data update

Task/Steffensens-method/Scala/steffensens-method.scala

@@ -0,0 +1,59 @@
+object Steffensen {
+
+  def aitken(p0: Double): Double = {
+    val p1 = f(p0)
+    val p2 = f(p1)
+    val p1m0 = p1 - p0
+    p0 - p1m0 * p1m0 / (p2 - 2.0 * p1 + p0)
+  }
+
+  def steffensenAitken(pinit: Double, tol: Double, maxiter: Int): Option[Double] = {
+    var p0 = pinit
+    var p = aitken(p0)
+    var iter = 1
+    while (math.abs(p - p0) > tol && iter < maxiter) {
+      p0 = p
+      p = aitken(p0)
+      iter += 1
+    }
+    if (math.abs(p - p0) > tol) None else Some(p)
+  }
+
+  def deCasteljau(c0: Double, c1: Double, c2: Double, t: Double): Double = {
+    val s = 1.0 - t
+    val c01 = s * c0 + t * c1
+    val c12 = s * c1 + t * c2
+    s * c01 + t * c12
+  }
+
+  def xConvexLeftParabola(t: Double): Double = deCasteljau(2.0, -8.0, 2.0, t)
+
+  def yConvexRightParabola(t: Double): Double = deCasteljau(1.0, 2.0, 3.0, t)
+
+  def implicitEquation(x: Double, y: Double): Double = 5.0 * x * x + y - 5.0
+
+  def f(t: Double): Double = {
+    val x = xConvexLeftParabola(t)
+    val y = yConvexRightParabola(t)
+    implicitEquation(x, y) + t
+  }
+
+  def main(args: Array[String]): Unit = {
+    var t0 = 0.0
+    for (i <- 0 until 11) {
+      print(f"t0 = $t0%3.1f : ")
+      steffensenAitken(t0, 0.00000001, 1000) match {
+        case None => println("no answer")
+        case Some(t) =>
+          val x = xConvexLeftParabola(t)
+          val y = yConvexRightParabola(t)
+          if (math.abs(implicitEquation(x, y)) <= 0.000001) {
+            println(f"intersection at ($x%f, $y%f)")
+          } else {
+            println("spurious solution")
+          }
+      }
+      t0 += 0.1
+    }
+  }
+}