Data commit

Task/Steffensens-method/Java/steffensens-method.java

@@ -0,0 +1,68 @@
+import java.util.Optional;
+
+public class Steffensen {
+    static double aitken(double p0) {
+        double p1 = f(p0);
+        double p2 = f(p1);
+        double p1m0 = p1 - p0;
+        return p0 - p1m0 * p1m0 / (p2 - 2.0 * p1 + p0);
+    }
+
+    static Optional<Double> steffensenAitken(double pinit, double tol, int maxiter) {
+        double p0 = pinit;
+        double p = aitken(p0);
+        int iter = 1;
+        while (Math.abs(p - p0) > tol && iter < maxiter) {
+            p0 = p;
+            p = aitken(p0);
+            iter++;
+        }
+        if (Math.abs(p - p0) > tol) return Optional.empty();
+        return Optional.of(p);
+    }
+
+    static double deCasteljau(double c0, double c1, double c2, double t) {
+        double s = 1.0 - t;
+        double c01 = s * c0 + t * c1;
+        double c12 = s * c1 + t * c2;
+        return s * c01 + t * c12;
+    }
+
+    static double xConvexLeftParabola(double t) {
+        return deCasteljau(2.0, -8.0, 2.0, t);
+    }
+
+    static double yConvexRightParabola(double t) {
+        return deCasteljau(1.0, 2.0, 3.0, t);
+    }
+
+    static double implicitEquation(double x, double y) {
+        return 5.0 * x * x + y - 5.0;
+    }
+
+    static double f(double t) {
+        double x = xConvexLeftParabola(t);
+        double y = yConvexRightParabola(t);
+        return implicitEquation(x, y) + t;
+    }
+
+    public static void main(String[] args) {
+        double t0 = 0.0;
+        for (int i = 0; i < 11; ++i) {
+            System.out.printf("t0 = %3.1f : ", t0);
+            Optional<Double> t = steffensenAitken(t0, 0.00000001, 1000);
+            if (!t.isPresent()) {
+                System.out.println("no answer");
+            } else {
+                double x = xConvexLeftParabola(t.get());
+                double y = yConvexRightParabola(t.get());
+                if (Math.abs(implicitEquation(x, y)) <= 0.000001) {
+                    System.out.printf("intersection at (%f, %f)\n", x, y);
+                } else {
+                    System.out.println("spurious solution");
+                }
+            }
+            t0 += 0.1;
+        }
+    }
+}